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– Notice of Proposed Rule Making –

By this notice and the order linked below, the Court of Appeals for the Second Circuit publishes for comment a proposed amendment to Local Rule 46.2 (b) (6), (7), which addresses attorney discipline. The amendment provides a procedure by which a New York State attorney discipline authority may request expedited disclosure of confidential record for its use in a New York State attorney conduct investigation or proceeding. Click to see the Clerk’s order inviting comment and the proposed amendment. In accordance with 28 U.S.C. § 2971(b) and Fed. R. App. P. 47(a)(1), comments are invited on the proposed rule. Please submit comments to the Clerk of Court at 40 Foley Square, New York, NY 10007 or no later than December 1, 2021.

– Bankruptcy Judgeship Vacancy –

The United States District Court for the Southern District of New York, is accepting applications for a Bankruptcy Judge. For announcement, please click . For application, please click .

– Public Announcement –

Request for Public Comment on the Reappointment of Federal Public Defender
Lisa Peebles for the
Northern District of New York. Click .

– Paper Copies of Briefs and Appendices in Cases Heard Under the L.R. 34.2 (a)(1) Non-Argument Calendar No Longer Required –

Beginning September 1, 2021, the Court of Appeals will no longer require paper copies of briefs and appendices to be filed in cases in which a party seeks review of the denial of: a claim for asylum under the Immigration and Nationality Act (INA); a claim for withholding of removal under the INA; a claim for withholding or deferral of removal under the Convention Against Torture; or, a motion to reopen or reconsider an order involving one of the claims listed above. A paper copy of all court filings must continue to be served on a pro se litigant in all immigration cases. A pro se litigant may continue to submit filings via the [email protected] email or file paper documents with the Court. Only pro se litigants submitting filings may use the email address and should include the case number in the subject line of the email. Click for Chief Judge Debra Ann Livingston’s order.

– Procedure for Oral Argument at the United States Court of Appeals for the Second Circuit –

Chief Judge Debra Ann Livingston has announced that when the 2021 Term begins on August 16, 2021 oral arguments will be conducted in person at the Thurgood Marshall United States Courthouse, Room 1703. Counsel and pro se litigants are expected to appear in person but will be permitted to argue remotely upon a request establishing good cause.

Current conditions related to the Covid pandemic require that counsel appear with no more than one colleague to assist with the argument. Pro se litigants also may be accompanied by no more than one person in the courtroom.

Individuals who arrive at the courthouse for argument must meet the health screening requirements and entrance protocols specified at the entrance to the building. All persons must wear a mask at all times in the building, including in the courtroom and during oral argument.

Until the Covid infection rate declines, the courtroom will be closed to the public and others who may wish to attend argument. The Court will continue to offer a livestream audio of the oral arguments. Click for the link to the livestream audio.

All parties are advised that the Court may announce changes to the procedures for participating in oral argument on short notice based upon updated public health information.

– Court Operations at the United States Court of Appeals for the Second Circuit –

Chief Judge Debra Ann Livingston has announced that the 2021 Term will begin on August 16, 2021 with oral arguments conducted in person at the Thurgood Marshall United States Courthouse, Room 1703. Counsel and pro se litigants who are scheduled to argue will be expected to appear in person. The courtroom will be open to the public subject to conditions that will be determined prior to August 16, 2021. The Court will continue to offer a livestream audio of the oral arguments. Additional changes in the Court’s operations are listed below.

Court Hours and Access –
Individuals who meet the
health screening
requirements and
entrance protocols
specified at the
entrance to the building
may enter to conduct
business with the Court. Beginning Tuesday, July 6, 2021, the public counter located in Room 150 will be open to litigants and the public between 10:00 a.m. and 2:00 p.m. Only two people seeking staff assistance may be in the room at one time. In addition, only one person at a time may use a kiosk, and for a maximum of 30 minutes. Papers also may be deposited in the Court’s Night Box, located in the lobby of the Thurgood Marshall United States Court, 40 Foley Square, New York, NY.

Filing Pro se Papers – In addition to filing papers in Room 150 or in the Night Box, pro se papers may be emailed to . For new cases in which a docketing notice has not yet issued, opening papers may be emailed to . A pro se litigant who has no access to email may send a paper by ordinary mail to United States Court of Appeals for the Second Circuit, Clerk’s Office, Thurgood Marshall United States Courthouse, 40 Foley Square, New York, NY.

Resumption of Paper Copies Requirement – Effective July 6, 2021, the Court will resume the requirement that six paper copies of each brief be submitted in each appeal at the time the brief is electronically filed. See L.R. 31.1. In addition, a party represented by counsel must file six copies of the appendix, unless the case is proceeding on the original record without an appendix. See L.R. 30.1(b)(c). The six paper copy rule also applies to a supplemental and special appendix. See L.R. 30.1(g); 32.1(c). In addition, a party represented by counsel must submit six paper copies of the appendix, unless the case is proceeding on the original record without an appendix. A pro se litigant must submit three paper copies of the appendix in cases in which an appendix is required. See L.R. 30.1(b), (e).

Three paper copies of documents that exceed 50 pages must be submitted to the Court. L.R. 21.1(b); 27.1(a)(4). If a petition for rehearing en banc exceeds 50 pages, 15 paper copies of the petition must be submitted to the Court. See L.R. 35.1(c). Click
for Chief Judge Livingston’s order.

Sealed Documents – A party that wishes to file a sealed document and is unable to follow the usual paper protocol may contact the Clerk’s Office at 212.857.8610 and email the sealed document to .

– Announcement –

Chief Judge Debra Ann Livingston announces the death of Judge Robert A. Katzmann of the Court of Appeals. Click to read the public statement.

– Second Circuit’s Pro Bono Appellate Mediator Panel –

The Legal Affairs Committee is accepting applications for the Second Circuit’s Pro Bono Appellate Mediator Panel. The deadline is June 30, 2021. Please refer to the Court’s official announcement and application materials, which are available .

– Announcement –

Chief Judge Debra Ann
Livingston announces the
death of Judge Peter W.
Hall of the Court of
Appeals. Click
to read the
public statement.

– Applications for service on CJA Panel –

The Criminal Justice Act Committee of the United States Court of Appeals for the Second Circuit is accepting applications for service on the Court’s Criminal Justice Act Panel.
For announcement click , for application click

–
Notice Regarding Judiciary Cybersecurity Breach –

On January 6, 2021 the Judicial Conference of the United States announced that sealed, non-public documents stored on the Judiciary’s electronic case management system, CM/ECF, may be vulnerable to the “compromise involving SolarWinds Orion products that are currently being exploited by malicious actors” that the Department of Homeland Security announced last month.

Pursuant to its Local Rules, the Second Circuit Court of Appeals does not permit for filing any sealed documents in its CM/ECF system; nor are any sealed documents stored in the CM/ECF system. Sealed documents are filed by delivering them directly to the Clerk’s Office in paper or digital format. Sealed documents are then separately stored in the Clerk’s Office. LR 25.1(j)(2). These practices will continue going forward. 

–
Announcement –

Chief Judge Debra Ann Livingston announces the death of Judge Ralph K. Winter of the Court of Appeals. Click
to read the public statement.

–
Notice of Fee
Changes –

Effective December 1, 2020, the fee changes listed below will take effect following amendments to the Court of Appeals Miscellaneous Fee Schedule, issued pursuant to 28 U.S.C. § 1913.

Fee Type

Old Fee

New Fee

Search of Records
$31
$32

 

 
 

For Reproducing
Recordings of
Proceedings
(Magnetic argument
tapes, CDs)
$31
$32

 

 
 

For reproducing
record in any appeal
in which the court
of appeals does not
require an appendix
under FRAP 30(f) and
L.R. 30.1
$86
$89

 

 
 

Attorney Admission
$221
$221

 

 
 

For a duplicate
certificate of
admission of good
standing
$19
$20

The Fee Schedule listed
on the Court’s website will
be updated December 1, 2020
to reflect the changes.

–

Court of
Appeals Implements New
Electronic Case Management
System for Immigration
Petitions for Review

–

Beginning October 1, 2020,
all new Petitions for Review
of Board of Immigration
Appeals decisions must be
filed in the new Appellate
Case Management System
(ACMS).  Instructions for
how to file a case in ACMS
are
.  Chief Judge Debra
Ann Livingston has issued an

that directs all ACMS
filings are subject to the
electronic filing
requirements set out in the
Court’s LR 25.1, pending
further order of the Court.

In
immigration appeals from BIA
decisions commenced prior to
October 1, 2020, filings
will continue to be made in
the CM/ECF system.  All
appeals from district court
decisions and original
proceedings commenced at the
Court other than appeals
from BIA decisions will
continue to be filed in
CM/ECF.

A court
user’s PACER login
information will link to
ACMS. The “one free look”
policy remains in effect.
 Payments through pay.gov
will also continue as usual.

The Clerk’s Office will
conduct another virtual
training on Friday, October
9, 2020.  Those interested
should email Eniola Ajayi at
.

The Clerk’s Office will conduct another virtual training on Friday, October 9, 2020. Those interested should email Eniola Ajayi at .

–
Report by Chief
Judge Katzmann to Court of Appeals Colleagues
posted

–
to read
“A Report by Chief Judge Robert A. Katzmann
to Court of Appeals
Colleagues: Summing Up the
Past Seven Years.”

–
Court of Appeals to Implement New Electronic Case Management System for Immigration Petitions for Review –

On October 1, 2020, the Court of Appeals for the Second Circuit will begin using a new electronic case management system, called the Appellate Case Management System (ACMS) for the filing of Petitions for Review from Board of Immigration Appeals decisions.
All new cases must be filed in ACMS. Cases commenced with the filing of a Petition for Review prior to October 1, 2020 will continue to be processed in CM/ECF until further notice. All filings in a case commenced prior to October 1, 2020 must be made in CM/ECF.

Also beginning October 1, 2020, a court user’s PACER login information will link to ACMS. The “one free look” policy remains in effect. Payments through pay.gov will also continue as usual

A Filing User who wishes to see a virtual demonstration of the new system may contact Eniola Ajayi at [email protected] no later than September 21, 2020. Instructional materials will be available as the launch date approaches.

–
Court of Appeals to Reduce Number of Paper Copies of Briefs and Appendices –

On August 24, 2020, the Court of Appeals will reduce to three, from six, the number of paper copies of briefs that must be filed in each appeal. In addition, a party represented by counsel must now file
three
copies of the appendix,
unless the case is
proceeding on the original
record without an appendix.
See. L.R. 30.1(b), (e). This
reduction in the number of
briefs and appendices filed
will continue until further
order of the Court. Click
for Chief Judge Robert
A. Katzmann’s order.

–
Court of Appeals to Resume Paper Copies Filing Requirement –

On July 1, 2020, the Court of Appeals will resume requiring that parties file paper copies of briefs, appendices and documents that exceed 50 pages in length pursuant to the provisions of the Federal Rules of Appellate Procedure and the Court’s Local Rules.

Regarding briefs, appendices and documents longer than 50 pages that were, or will be, filed between March 26 and June 30, 2020, paper copies will be due no later than July 10, 2020, if the case is currently pending. Click for Chief Judge Robert A. Katzmann’s order.

The Court’s practice, previously announced on March 26, 2020, regarding the filings of pro se papers, petitions for review and petitions for a writ seeking extraordinary relief, that cannot be filed in ECF will continue: Pro se papers may be emailed to .
For new cases in which a docketing notice has not yet issued, opening papers may be emailed to . A pro se litigant who has no access to email may send a paper by ordinary mail. Papers also may be deposited in the Court’s Night Box, located in the lobby of the Thurgood Marshall United States Courthouse, 40 Foley Square, New York, NY.

Sealed Documents. A party that wishes to file a sealed document and is unable to follow the usual paper protocol may contact the Clerk’s Office at 646.584.2696 and email the sealed document to .

–
Applications for Second Circuit Pro Bono Appellate Mediator Panel –

The deadline for applications for appointment to the Second Circuit’s Pro Bono Appellate Mediator Panel in 2020 is extended to July 8, 2020. Application materials should be submitted to: . Please refer to the Court’s official announcement and application materials, which are available .

Chief Judge Robert A. Katzmann
thanks the members of the
Criminal Justice Act Panels
throughout the Circuit for
their continued dedication
and commitment to the
representation of the
indigent during these
difficult times, and
reiterates the Court’s
policy of accepting motions
seeking approval of interim
payments under the Court’s
Amended CJA Plan [Section X,
Paragraph F]. 

–
Operations Continue at the United States Court of Appeals for the Second Circuit –

The regular argued appeals and motions calendars continue to be heard as scheduled. As explained below, parties are expected to begin filing papers on April 6, 2020 pursuant to the Court’s March 16, 2020 order.

Document Filings and Form Deadlines – On March 16, 2020 the Second Circuit ordered a 21-day extension of time for all filings and deadlines. Filing dates set specifically by order after March 13, 2020 and the filing date for a notice of appeal or other document that confers jurisdiction on the Court were not covered by the March 16th order.

Applying the 21-day extension, filings and deadlines that were originally due between March 16 and May 17, 2020 are now due beginning April 6, 2020 and ending June 5, 2020. Absent an extraordinary circumstance, which is defined as ‘serious personal illness or death in counsel’s immediate family’, no additional extensions of time to file will be granted. Local Rule 27.1 (f)(1). Papers and deadlines that are due on May 18, 2020 and thereafter are due on the date specified in an order or rule. The Court does not anticipate issuing an order that further extends all filing dates and other deadlines.

– On March 16, 2020 the Second Circuit ordered a 21-day extension of time for all filings and deadlines. Filing dates set specifically by order after March 13, 2020 and the filing date for a notice of appeal or other document that confers jurisdiction on the Court were not covered by the March 16th order.Applying the 21-day extension, filings and deadlines that were originally due between March 16 and May 17, 2020 are now due beginning April 6, 2020 and ending June 5, 2020. Absent an extraordinary circumstance, which is defined as ‘serious personal illness or death in counsel’s immediate family’, no additional extensions of time to file will be granted. Local Rule 27.1 (f)(1). Papers and deadlines that are due on May 18, 2020 and thereafter are due on the date specified in an order or rule. The Court does not anticipate issuing an order that further extends all filing dates and other deadlines.

 

Paper Copies. In the
Court’s continuing effort to
adapt its operations during
the COVID-19 pandemic, paper
copies of documents that are
otherwise required to
complete a filing will not
be required in any case
pending further order or
upon the specific request of
the Clerk. Paper copies of
documents must continue to
be served on pro se
litigants and others who are
not Filing Users as defined
in Local Rule 25.1
(a)(1)(D). Click for
Chief Judge Robert A.
Katzmann’s order.

 

Papers, such as pro se
papers, petitions for
review, and petitions for a
writ seeking extraordinary
relief, that cannot be filed
in ECF, should be emailed as
follows: Pro se papers may
be emailed to .
For new cases in which a
docketing notice has not yet
issued, opening papers may
be emailed to
. 
A pro se litigant who has no
access to email may send a
paper request by ordinary
mail. Papers also may be
deposited in the Court’s
Night Box, located in the
lobby of the Thurgood
Marshall United States
Courthouse, 40 Foley Square,
New York, NY.

Papers, such as pro se papers, petitions for review, and petitions for a writ seeking extraordinary relief, that cannot be filed in ECF, should be emailed as follows: Pro se papers may be emailed to . For new cases in which a docketing notice has not yet issued, opening papers may be emailed to . A pro se litigant who has no access to email may send a paper request by ordinary mail. Papers also may be deposited in the Court’s Night Box, located in the lobby of the Thurgood Marshall United States Courthouse, 40 Foley Square, New York, NY.

Sealed Documents. A
party that wishes to file a
sealed document and is
unable to follow the usual
paper protocol may contact
the Clerk’s Office at
646.584.2696 and email the
sealed document to

–
Oral Arguments at the Second Circuit –

The regular argued appeals and motions calendars continue to be heard as scheduled. Effective Monday, March 23, 2020 and until the COVID-19 crisis passes, the Court will hear all oral arguments using a teleconference platform. All lawyers and pro se litigants who are scheduled to argue must do so by teleconference. The Clerk’s Office will forward teleconference instructions to the lawyers and pro se litigants appearing each argument day. In the alternative, parties may request to submit the appeal for determination.

All oral arguments will be audio livestreamed. Click for the livestream link.

– Operations at the Second Circuit to Address COVID-19 Pandemic –

As the limitations on social interactions in public spaces continue to expand to address the spread of COVID-19, the United States Court of Appeals for the Second Circuit will remain open to fulfill its constitutional and statutory responsibilities and is adapting its operations as follows:

Oral Arguments – The regular argued appeals and motions calendars will be heard as scheduled. A lawyer or pro se litigant who is scheduled to argue and wishes to do so in person may appear at the Thurgood Marshall United States Courthouse,
40 Foley Square, New York, NY, Room 1703. In addition, the Court has established a teleconference platform for judges and persons scheduled to argue who wish to appear remotely. To arrange for an appearance by audio, a lawyer scheduled to argue should electronically file a letter request.
A pro se litigant should email the request to and call 212.857.8500. The Clerk’s Office will forward teleconference instructions to the requester.
Parties to all appeals are reminded that at the discretion of the panel any appeal that meets the standard set out in the Federal Rules of Appellate Procedure 34(a)(2) may be taken on submission.

Access to the Courthouse – Individuals who do not have business with the Court will not be admitted until further order of the Court. Individuals who seek access to the Thurgood Marshall United States Courthouse to transact business with the Court must,
in the judgment of the courthouse security officers, meet the health standards specified at the entrance to the courthouse. To preserve public access to the Court’s oral arguments, the audio of arguments will be live streamed.
for the link to the live steam. for Chief Judge Robert A. Katzmann’s order regarding access to the courthouse.

Filings – The national response to the pandemic will disrupt the ordinary course of all business activity, including the operation of the Judiciary. To minimize the disruption and assist the Court in managing Court business, all filing dates and other deadlines set out in the
Federal Rules of Appellate Procedure, the Court’s Local Rules and the Court’s orders are extended or tolled by 21 days, effective today through May 17, 2020. For example, a notice of appearance or scheduling notification currently due on March 18th is now due on April 8th. A brief currently due on April 15th is now due May 6th.
However, a brief due on May 20th continues to be due on May 20th.
&nbsp&nbsp&nbsp

Notwithstanding this general extension, a judge or panel may, by separate order, direct the parties to comply with a different filing date as deemed necessary in a particular case. In addition, in counseled civil cases the automatic dismissal provision in the order
that set the original filing date remains in effect.
&nbsp&nbsp&nbsp

The due date for a notice of appeal, petition for review or other document that confers jurisdiction on the Court is not affected by this order. The filing dates for those papers remain as stated in the statute or rule that confers jurisdiction.
for Chief Judge Robert A. Katzmann’s Order.

Court Hours and Staffing – Though the Court continues to be open, people are encouraged to email correspondence and filings that cannot be filed in ECF. These documents include pro se papers, petitions for review, and petitions for a writ seeking extraordinary relief. Pro se papers may be emailed to
. In new cases in which a docketing notice has not yet issued, opening papers may be emailed to . A pro se litigant who has no access to
email may send a paper request by ordinary mail. Papers also may be deposited in the Court’s Night Box, located in the lobby of the Thurgood Marshall United States Courthouse, 40 Foley Square, New York, NY.

The majority of court staff are teleworking each day. A skeletal staff will report to the Courthouse to perform tasks that cannot be done remotely. Tasks will be prioritized, but it is likely that the response to some inquiries may be delayed. The telephone numbers set out on the
Clerk’s Office Directory Screen will remain operational.

Emergency Applications – A lawyer or litigant who seeks to file a request for an emergency stay or relief that requires immediate attention shall file the request according to the directions set out in this notice and contact the Clerk of Court at 646.584.2696.

Further Updates – Because the national response to the COVID-19 pandemic continues to change, please check this website as the Court adapts its operations to conform to additional developments.

–
Second Circuit Calendars –
The regular argued appeals and motions calendars will be heard as scheduled at the United States Court of
Appeals for the Second Circuit.

A lawyer or pro se party scheduled to
argue is directed to contact the Clerk of Court at
646.584.2696 if she or he has
* visited China, Iran, Italy, Japan or South Korea within the last 14 days,
    

* been in close contact with a person who has visited a listed country within the last 14 days,

   

* been asked to self-quarantine by a health official,

* been diagnosed with COVID-19, or been in contact with a person diagnosed with COVID-19, or

   

* a verifiable health condition, specifically chronic lung disease, cancer, diabetes, heart disease or a weakened immune system.

 

–
The Legal Affairs Committee –

is accepting applications for the Second Circuit’s Pro Bono Appellate Mediator Panel. The deadline is May 8, 2020. Please refer to the Court’s official announcement and application materials which are available
.

–
Amendments to the Federal Rules of Appellate Procedure –

On December 1, 2019, amendments to the Federal Rules of Appellate Procedure will take effect. The rules impacted are 3, 5, 13, 21, 25, 26, 26.1, 28, 32, and 39. Among the changes are the elimination of proofs of service when documents are electronically filed and the addition of new sub-sections (b) and (c) for Rule 26.1 disclosure statements.
For announcement click

– Pearl Street Entrance to Thurgood Marshall U.S. Courthouse Closed –

Effective today, the Pearl Street entrance to the Thurgood Marshall U.S. Courthouse will be closed to the public to facilitate repair of the elevators. Only visitors who require wheelchair assistance or who have difficulty walking up stairs may use the Pearl Street entrance. All other visitors must use the Centre Street entrance.

– Press Release –

Chief Judge Robert A. Katzmann has announced the appointment of Michael D. Jordan to be the Circuit Executive for the Second Circuit.
to read the press release.

–
Amendment to the Local Rules of the Second Circuit –

The Court of Appeals for the Second Circuit has amended Local Rule 31.2(a)(2), effective June 13, 2019, which governs the time to file reply briefs. The time to file an Oral Argument Statement, Local Rule 34.1(a), has not been amended. Click
for the order adopting the amendment.

–
Notice of proposed rulemaking –

By this notice and the order linked below, the Court of Appeals for the Second Circuit publishes for comment proposed amendments to
Local Rules 31.2(2) and 34.1, which govern the time to file a reply brief and an oral argument statement, respectively. The amendments
provide that a reply brief be filed within 21 days of filing the last appellee’s brief and an oral argument statement be filed within
7 days of filing the last appellee’s brief. Click

to view the Court’s order inviting comment and the proposed amendment. In accordance with 28 U.S.C. § 2071(b) and Fed. R. App. P. 47(a)(1),
comments are invited on the proposed rule. Please submit comments to the Clerk of Court at 40 Foley Square, New York, NY 10007 or
no later than April 25, 2019.

–
The Legal Affairs Committee –

is accepting applications for the Second Circuit’s Pro Bono Appellate Mediator Panel. The deadline is May 1, 2019. Please refer to the Court’s official announcement and application materials, which are available

–
Notice to the Bar –
Although an
appropriation or continuing
resolution funding the
operations of the federal
government, including the
United States Courts, was
not enacted by midnight
December 21, 2018 the United
States Court of Appeals for
the Second Circuit will
continue to resolve cases
and controversies as
mandated by the
Constitution. Click
for Chief Judge Katzmann’s order.

 

Specifically,
the Court will docket new cases, receive documents for filing,
determine motions,
hear cases on
submission and by
argument as scheduled,
and decide cases for
the duration of the
appropriations
lapse. Cases
scheduled to
be heard
during this
period will
go forward
unless the
panel for a
case directs
otherwise.       

 

Chief Judge Katzmann has
issued an order
directing
that in
cases in
which a
party is
represented
by a lawyer
employed by
the federal
government,
the filing
requirements
specified in
the Federal
Rules of
Appellate
Procedure
and this
Court’s
Local Rules
will be
tolled for
the duration
of the
lapse. The
time to file
will resume
two business
days after a budget
appropriation or
continuing
resolution
is enacted
into law.
For example, if on
December 21,
2018 ten
days had run
on a party’s
time to file
a paper and
if, on
Thursday,
January 3,
2019 a
budget is
enacted, the
time to file
will resume
running at
12:01 a.m.
on Tuesday,
January 8,
2019 as the
eleventh day
in the
filing
period.
Click
for Chief Judge Katzmann’s order regarding filing deadlines.

 

In
cases
subject to
the order,
the
obligation
of other
parties to
comply with
the filing
requirements
of the
Federal
Rules of
Appellate
Procedure
and this
Court’s
Local Rules
remains in
effect.
Pursuant to
the order,
the Court
retains
discretion
to issue
specific
directions
as may be
necessary in
particular
cases.

 

– Amendment to the Local Rules of the Second Circuit
– The Court of Appeals for the Second Circuit has amended Local Rule 27.1(j), effective December 17, 2018, which governs motions. Click
for the order adopting the amendment.

 

– Notice of proposed rulemaking – By this notice and the order linked below, the Court of Appeals for the Second Circuit publishes for comment a proposed amendment to Local Rule 27.1, which governs motions. The amendment provides that a party in a proceeding covered by Federal Rule of Civil Procedure 5.2(c) may file a motion to abbreviate the party’s name in the Court’s opinion or summary order and sets the time within which such a motion must be filed. Click to view the Court’s order inviting comment and the proposed amendment. In accordance with 28 U.S.C. § 2071(b) and Fed. R. App. P. 47(a)(1), comments are invited on the proposed rule. Please submit comments to the Clerk of Court at 40 Foley Square, New York, NY 10007 or no later than November 29, 2018.

 

– Chief Judge 2018 State of the Circuit Report – Click .

 

– 2018 Justice For All Annual Report –
to read the 2018 Justice For All annual report.

 

– Notice of Fee Changes – Effective September 1, 2018, the fee changes listed below will take effect pursuant to amendments to the Court of Appeals Miscellaneous Fee Schedule, issued pursuant
to 28 U.S.C. § 1913.

Old Fee:

Reproduction (documents)
 50¢ per page

 

New Fee:

Reproduction (documents) in paper form
  50¢ per page

Reproduction of electronic records stored outside of the court’s electronic case management system, including but not limited to, document files, audio and video recordings (other than a recording of a court proceeding)

  $31 per record

 

The Fee Schedule listed on the Court’s website will be updated September 1, 2018, to reflect the changes.

 

– New Federal Law Clerk Hiring Plan – The Second Circuit is adhering to the new Federal Law Clerk Hiring Plan. Click for the plan.

 

– Chief Judge Robert A. Katzmann has announced the unveiling of the for Justice for All: Courts and the Community , the civic education initiative of the federal courts of the Second Circuit. Our mission is to increase public understanding of the role of the courts, and to bring courts closer to the community.
Click for the announcement.

 

 

Announcements Archive 

 

 

Second Order Differential Equations

Here we learn how to solve equations of this type:

d2ydx2 + pdydx + qy = 0

Differential Equation

A Differential Equation is an equation with a function and one or more of its derivatives:

Example: an equation with the function y and its
derivative dy dx  

Order

The Order is the highest derivative (is it a first derivative? a second derivative? etc):

Example:

dydx + y2 = 5x

It has only the first derivative dy dx , so is “First Order”

Example:

d2ydx2 + xy = sin(x)

This has a second derivative d2y dx2 , so is “Second Order” or “Order 2”

Example:

d3ydx3 + xdydx + y = ex

This has a third derivative d3y dx3 which outranks the dy dx , so is “Third Order” or “Order 3”

Before tackling second order differential equations, make sure you are familiar with the various methods for solving first order differential equations.

Second Order Differential Equations

We can solve a second order differential equation of the type:

d2ydx2 + P(x)dydx + Q(x)y
= f(x)

where P(x), Q(x) and f(x) are functions of x, by using:

Undetermined Coefficients which only works when f(x) is a polynomial, exponential, sine, cosine or a linear combination of those.

Variation of Parameters which is a little messier but works on a wider range of functions.

But here we begin by learning the case where f(x) = 0 (this makes it “homogeneous”):

d2ydx2 + P(x)dydx + Q(x)y
= 0

and also where the functions P(X) and Q(x) are constants p and q:

d2ydx2 + pdydx + qy = 0

Let’s learn to solve them!

 

to the rescue

We are going to use a special property of the derivative of the exponential function:

At any point the slope (derivative) of x equals the value of x :

And when we introduce a value “r” like this:

f(x) = erx

We find:

• the first derivative is f'(x) = rerx
• the second derivative is f”(x) = r2erx

In other words, the first and second derivatives of f(x) are both multiples of f(x)

This is going to help us a lot!

Example 1: Solve

d2ydx2 + dydx − 6y = 0

Let y = erx so we get:

• dydx

  = rerx

• d2ydx2

  = r2erx

Substitute these into the equation above:

r2erx + rerx − 6erx = 0

Simplify:

erx(r2 + r − 6) = 0

r2 + r − 6 = 0

We have reduced the differential equation to an ordinary quadratic equation!

This quadratic equation is given the special name of characteristic equation.

We can factor this one to:

(r − 2)(r + 3) = 0

So r = 2 or −3

And so we have two solutions:

y = e2x

y = e−3x

But that’s not the final answer because we can combine different multiples of these two answers to get a more general solution:

y = Ae2x + Be−3x

Check

Let us check that answer. First take derivatives:

y = Ae2x + Be−3x

dydx = 2Ae2x − 3Be−3x

d2ydx2 = 4Ae2x + 9Be−3x

Now substitute into the original equation:

d2ydx2 + dydx − 6y = 0

(4Ae2x + 9Be−3x) + (2Ae2x − 3Be−3x) − 6(Ae2x + Be−3x) = 0

4Ae2x + 9Be−3x + 2Ae2x − 3Be−3x − 6Ae2x − 6Be−3x = 0

4Ae2x + 2Ae2x − 6Ae2x+ 9Be−3x− 3Be−3x − 6Be−3x = 0

0 = 0

It worked!

So, does this method work generally?

Well, yes and no. The answer to this question depends on the constants p and q.

With y = erx as a solution of the differential equation:

d2ydx2 + pdydx + qy = 0

we get:

r2erx + prerx + qerx = 0

erx(r2 + pr + q) = 0

r2 + pr + q = 0

This is a quadratic equation, and there can be three types of answer:

• two real roots
• one real root (i.e. both real roots are the same)
• two complex roots

How we solve it depends which type!

We can easily find which type by calculating the discriminant p2 − 4q. When it is

• positive we get two real roots
• zero we get one real root
• negative we get two complex roots

Two Real Roots

When the discriminant p2 − 4q is positive we can go straight from the differential equation

d2ydx2 + pdydx + qy = 0

through the “characteristic equation”:

r2 + pr + q = 0

to the general solution with two real roots r1 and r2:

y = Aer1x + Ber2x

Example 2: Solve

d2ydx2 − 9dydx + 20y = 0

The characteristic equation is:

r2 − 9r + 20 = 0

Factor:

(r − 4)(r − 5) = 0

r = 4 or 5

So the general solution of our differential equation is:

y = Ae4x + Be5x

And here are some sample values:

Example 3: Solve

6d2ydx2 + 5dydx − 6y = 0

The characteristic equation is:

6r2 + 5r − 6 = 0

Factor:

(3r − 2)(2r + 3) = 0

r = 23 or −32

So the general solution of our differential equation is:

y = Ae(23x) + Be(−32x)

Example 4: Solve

9d2ydx2 − 6dydx − y = 0

The characteristic equation is:

9r2 − 6r − 1 = 0

This does not factor easily, so we use the quadratic equation formula:

x = −b ± √(b2 − 4ac) 2a

with a = 9, b = −6 and c = −1

x = −(−6) ± √((−6)2 − 4×9×(−1)) 2×9

x = 6 ± √(36+ 36) 18

x = 6 ± 6√2 18

x = 1 ± √2 3

So the general solution of the differential equation is

y = Ae(1 + √2 3)x + Be(1 − √2 3)x

One Real Root

When the discriminant p2 − 4q is zero we get one real root (i.e. both real roots are equal).

Here are some examples:

Example 5: Solve

d2ydx2 − 10dydx + 25y = 0

The characteristic equation is:

r2 − 10r + 25 = 0

Factor:

(r − 5)(r − 5) = 0

r = 5

So we have one solution: y = e5x

 

BUT when e5x is a solution, then xe5x is also a solution!

Why? I can show you:

y = xe5x

dydx = e5x + 5xe5x

d2ydx2 = 5e5x + 5e5x + 25xe5x

So

d2ydx2 − 10dydx + 25y

= 5e5x + 5e5x + 25xe5x − 10(e5x + 5xe5x) + 25xe5x

= (5e5x + 5e5x − 10e5x) + (25xe5x − 50xe5x + 25xe5x) = 0

So, in this case our solution is:

y = Ae5x + Bxe5x

 

How does this work in the general case?

With y = xerx we get the derivatives:

• dydx

  = erx + rxerx

• d2ydx2

  = rerx + rerx + r2xerx

So

d2ydx2 + p dydx + qy

= (rerx + rerx + r2xerx) + p( erx + rxerx ) + q( xerx )

= erx(r + r + r2x + p + prx + qx)

= erx(2r + p + x(r2 + pr + q))

= erx(2r + p) because we already know that r2 + pr + q = 0

 

And when r2 + pr + q has a repeated root, then r = −p2 and 2r + p = 0

So if r is a repeated root of the characteristic equation, then the general solution is

y = Aerx + Bxerx

Let’s try another example to see how quickly we can get a solution:

Example 6: Solve

4d2ydx2 + 4dydx + y = 0

The characteristic equation is:

4r2 + 4r + 1 = 0

Then:

(2r + 1)2 = 0

r = −12

So the solution of the differential equation is:

y = Ae(−½)x + Bxe(−½)x

Complex roots

When the discriminant p2 − 4q is negative we get complex roots.

Let’s try an example to help us work out how to do this type:

Example 7: Solve

d2ydx2 − 4dydx + 13y = 0

The characteristic equation is:

r2 − 4r + 13 = 0

This does not factor, so we use the quadratic equation formula:

x = −b ± √(b2 − 4ac) 2a

with a = 1, b = −4 and c = 13

x = −(−4) ± √((−4)2 − 4×1×13) 2×1

x = 4 ± √(16− 52) 2

x = 4 ± √(−36) 2

x = 4 ± 6i 2

x = 2 ± 3i

If we follow the method used for two real roots, then we can try the solution:

y = Ae(2+3i)x + Be(2−3i)x

We can simplify this since e2x is a common factor:

y = e2x( Ae3ix + Be−3ix )

But we haven’t finished yet … !

Euler’s formula tells us that:

eix = cos(x) + i sin(x)

So now we can follow a whole new avenue to (eventually) make things simpler.

Looking just at the “A plus B” part:

Ae3ix + Be−3ix

A(cos(3x) + i sin(3x)) + B(cos(−3x) + i sin(−3x))

Acos(3x) + Bcos(−3x) + i(Asin(3x) + Bsin(−3x))

Now apply the Trigonometric Identities: cos(−θ)=cos(θ) and sin(−θ)=−sin(θ):

Acos(3x) + Bcos(3x) + i(Asin(3x) − Bsin(3x)

(A+B)cos(3x) + i(A−B)sin(3x)

Replace A+B by C, and A−B by D:

Ccos(3x) + iDsin(3x)

And we get the solution:

y = e2x( Ccos(3x) + iDsin(3x) )

 

Check

We have our answer, but maybe we should check that it does indeed satisfy the original equation:

y = e2x( Ccos(3x) + iDsin(3x) )

dydx = e2x( −3Csin(3x)+3iDcos(3x) ) + 2e2x( Ccos(3x)+iDsin(3x) )

d2ydx2 = e2x( −(6C+9iD)sin(3x) + (−9C+6iD)cos(3x)) + 2e2x(2C+3iD)cos(3x) + (−3C+2iD)sin(3x) )

Substitute:

d2ydx2 − 4dydx + 13y = e2x( −(6C+9iD)sin(3x) + (−9C+6iD)cos(3x)) + 2e2x(2C+3iD)cos(3x) + (−3C+2iD)sin(3x) ) − 4( e2x( −3Csin(3x)+3iDcos(3x) ) + 2e2x( Ccos(3x)+iDsin(3x) ) ) + 13( e2x(Ccos(3x) + iDsin(3x)) )

… hey, why don’t YOU try adding up all the terms to see if they equal zero … if not please let me know, OK?

How do we generalize this?

Generally, when we solve the characteristic equation with complex roots, we will get two solutions r1 = v + wi and r2 = v − wi

So the general solution of the differential equation is

y = evx ( Ccos(wx) + iDsin(wx) )

Example 8: Solve

d2ydx2 − 6dydx + 25y = 0

The characteristic equation is:

r2 − 6r + 25 = 0

Use the quadratic equation formula:

x = −b ± √(b2 − 4ac) 2a

with a = 1, b = −6 and c = 25

x = −(−6) ± √((−6)2 − 4×1×25) 2×1

x = 6 ± √(36− 100) 2

x = 6 ± √(−64) 2

x = 6 ± 8i 2

x = 3 ± 4i

And we get the solution:

y = e3x(Ccos(4x) + iDsin(4x))

Example 9: Solve

9d2ydx2 + 12dydx + 29y = 0

The characteristic equation is:

9r2 + 12r + 29 = 0

Use the quadratic equation formula:

x = −b ± √(b2 − 4ac) 2a

with a = 9, b = 12 and c = 29

x = −12 ± √(122 − 4×9×29) 2×9

x = −12 ± √(144− 1044) 18

x = −12 ± √(−900) 18

x = −12 ± 30i 18

x = −23
± 53i

And we get the solution:

y = e(−23)x(Ccos(53x) + iDsin(53x))

Summary

To solve a linear second order differential equation of the form

d2ydx2 + pdydx + qy = 0

where p and q are constants, we must find the roots of the characteristic equation

r2 + pr + q = 0

There are three cases, depending on the discriminant p2 – 4q. When it is

positive we get two real roots, and the solution is

y = Aer1x + Ber2x

zero we get one real root, and the solution is

y = Aerx + Bxerx

negative we get two complex roots r1 = v + wi and r2 = v − wi, and the solution is

y = evx ( Ccos(wx) + iDsin(wx) )

 

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