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##### MATH 4027 - Ordinary Differential Equations - LSU Study Resources
• 10 Pages
###### FinalExamPractice

School: LSU

Course: Ordinary Differential Equations

Final Exam Practice Problems Math 4027 The nal exam will be comprehensive. You should review both the statements of all existence and uniqueness theorems and the various techniques employed for nding solution of dierential equations. As with the second ex

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###### DE11

School: LSU

Course: Ordinary Differential Equations

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###### DE10

School: LSU

Course: Ordinary Differential Equations

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###### DE12

School: LSU

Course: Ordinary Differential Equations

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###### DE13

School: LSU

Course: Ordinary Differential Equations

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• ###### Ordinary Differential Equations
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###### Ordinary Differential Equations

School: LSU

Course: Ordinary Differential Equations

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###### DE14

School: LSU

Course: Ordinary Differential Equations

• 3 Pages
###### ExerciseSet4s07a

School: LSU

Course: Differential Equations

Exercise Set 4 Math 4027 Due: February 15, 2007 For each of the following matrices A, do all of the following calculations: (a) Compute the eigenvalues of A. For convenience, the characteristic polynomial cA () = det(A I ) is given. (b) Find all of the ei

• 6 Pages
###### ExerciseSet5s07a

School: LSU

Course: Differential Equations

Exercise Set 5 Math 4027 Due: March 1, 2007 From Waltman, Section 7. 1. Find eAt where (a) A = 11 . 01 Solution. The matrix A is triangular, so the eigenvalues are the diagonal entries, i.e., 1 = 2 = 1. From Theorem 7.1, we need to solve the system of die

• 2 Pages
###### ExerciseSet6s07a

School: LSU

Course: Differential Equations

Exercise Set 6 Math 4027 Due: March 21, 2007 Find the general solution of the given dierential equation. 1. 4y + y = 0 Solution. The characteristic polynomial is p() = 42 + = (4 + 1) so the roots of p() = 0 are 1 = 0 and 2 = 1/4 so the solution of the die

• 2 Pages
###### ExerciseSet7s07a

School: LSU

Course: Differential Equations

Exercise Set 7 Math 4027 Due: April 10, 2007 From Waltman, Page 107. 6. Locate the critical points of the following systems. (a) cfw_(n, 0) : n Z (b) (0, 0) and (1, 1) (c) cfw_(0, y ) : y R (d) (0, 0) and (1 2, 1) (e) (0, 0), (1, 1), and (1, 1) (f) cfw_(

• 4 Pages
###### ExerciseSet8s07a

School: LSU

Course: Differential Equations

Exercise Set 8 Math 4027 Due: April 19, 2007 1. Consider the three systems (a) x y = 2x + y = y + x2 (b) x y = 2x + y = y + x2 (c) x y = 2x + y = y x2 All three have a critical point at the origin (0, 0). Which two systems have the same qualitative struct

• 5 Pages
###### Exam 1

School: LSU

Course: Differential Equations

Name: Exam 1 Instructions. Answer each of the questions on your own paper. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. Put your name on each

• 5 Pages
###### Exam 2

School: LSU

Course: Differential Equations

Name: Exam 2 Instructions. Answer each of the questions on your own paper, except for problem 2, where you may record your answers in the box provided. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given f

• 3 Pages
###### Exam1Reviews07a

School: LSU

Course: Differential Equations

Math 4027 Exam 1 Review Sheet Review Exercises for Exam 1 Answers 1. (a) y (t) = ce2t (b) y (t) = ce2t + et (c) y (t) = cet + 1 e3t 2 2 (d) y (t) = cet + (e) y (t) = ct3 t 1 2 3 cos t 2. (a) y (t) = 5te2t e2t (b) y (t) = 2e3t cos 2t + e3t (c) y (t) = t4

• 6 Pages
###### Exam2Reviews07a

School: LSU

Course: Differential Equations

Math 4027 Exam 2 Review Sheet Exam 2 will be on Tuesday, April 24, 2007. The syllabus for this exam consists of Sections 9 (Elementary Stability) and 11 (Scalar Equations) of Chapter 1 and Sections 1 6 and 8 of Chapter 2 in Waltman. You will be allowed (

• 4 Pages
###### ExerciseSet2s07a

School: LSU

Course: Differential Equations

Exercise Set 2 Math 4027 Due: January 25, 2007 1. Find the solution of the initial value problems: (a) y + 2y = x, y (0) = 1, Solution. Multiply by e2x to get (e2x y ) = xe2x and then integrate to get e2x y = x 2x 1 2x e e + C. 2 4 Solve for y and substit

• 4 Pages
###### ExerciseSet3s07a

School: LSU

Course: Differential Equations

Exercise Set 3 Math 4027 Due: February 6, 2007 Pages 1314. 7. Construct the inverse of each of the given matrices. You may use any of the techniques that you learned in linear algebra for the computation of the inverse A1 of a square matrix. The two most

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###### DE9

School: LSU

Course: Ordinary Differential Equations

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###### DE8

School: LSU

Course: Ordinary Differential Equations

• 5 Pages
###### Exercise Set 5

School: LSU

Course: Ordinary Differential Equations

Exercise Set 5 Math 4027 Due: May 5, 2005 1. Solve the following dierential equations: (a) y = x2 /y . Solution. The equation is separable, so rewrite it in the form yy = x2 or in dierential form y dy = x2 dx and integrate to get an implicit equation y2 x

• 3 Pages
###### Exercise Set 4

School: LSU

Course: Ordinary Differential Equations

Exercise Set 4 Math 4027 Due: April 7, 2005 1. Find the general solution of each of the following dierential equations. (a) 2x2 y + xy y = 0 Solution. The indicial equation q (r) = 2r(r 1) + r 1 = (2r + 1)(r 1) has roots 1 and 1/2. Hence y = c1 x + c2 |x|

• 4 Pages
###### Exercise Set 3

School: LSU

Course: Ordinary Differential Equations

Exercise Set 3 Math 4027 Due: March 15, 2005 1. Verify that the function 1 (x) is a solution of the given dierential equation, and nd a second linearly independent solution 2 (x) on the interval indicated. (a) y 2x2 y = 0 (b) y 4xy + (4x2 2)y = 0 (c) (1 x

• 3 Pages
###### Exercise Set 2

School: LSU

Course: Ordinary Differential Equations

Exercise Set 2 Math 4027 Due: February 10, 2005 1. Determine, with justication, whether each of the following lists of functions is linearly dependent or linearly independent. (a) 1 (x) = ex , 2 (x) = ex+2 Solution. These functions are linearly dependent

• 3 Pages
###### Exercise Set 1

School: LSU

Course: Ordinary Differential Equations

Exercise Set 1 Math 4027 Due: February 1, 2005 1. Find the solution of the initial value problems: (a) y + 2y = x, y (0) = 1, Solution. Multiply by e2x to get (e2x y ) = xe2x and then integrate to get x 2x 1 2x e e + C. 2 4 Solve for y and substitute y (0

• 5 Pages
###### Exam 2

School: LSU

Course: Ordinary Differential Equations

Name: Exam 2 Instructions. Answer each of the questions on your own paper. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. Put your name on each

• 6 Pages
###### Exam 1

School: LSU

Course: Ordinary Differential Equations

Name: Exam 1 Instructions. Answer each of the questions on your own paper. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. Put your name on each

• 2 Pages
###### Exam 1 Solutions

School: LSU

Course: Ordinary Differential Equations

• 12 Pages
###### Exam2Practice

School: LSU

Course: Ordinary Differential Equations

Exam II Practice Problems Math 4027 The syllabus for the second exam will consist of Chapter 3 (Sections 1 8) and Chapter 4 (Sections 1 4, 6 8). Here are a few sample problems similar to previously assigned problems. 1. Find a basis for the solution set o

• 2 Pages
###### Diff Eq.

School: LSU

Course: Ordinary Differential Equations

Math 4027 Differential Equations Spring 2005 TTh 10:40 - 12:00 Lockett 113 Instructor: William A. Adkins 350 Lockett Hall Tel: 578-1601 E-mail: adkins@math.lsu.edu Class Web Site: http:/www.math.lsu.edu/~adkins/m4027.html Office Hours: 9:40 - 10:30 A.M. M

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###### DE1

School: LSU

Course: Ordinary Differential Equations

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###### DE3

School: LSU

Course: Ordinary Differential Equations

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###### DE2

School: LSU

Course: Ordinary Differential Equations

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###### DE4

School: LSU

Course: Ordinary Differential Equations

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###### DE5

School: LSU

Course: Ordinary Differential Equations

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###### DE7

School: LSU

Course: Ordinary Differential Equations

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###### DE6

School: LSU

Course: Ordinary Differential Equations

• 4 Pages
###### Homework Solution 2

School: LSU

Course: Differential Equations

Exercise Set 2 Math 4027 Due: January 25, 2007 1. Find the solution of the initial value problems: (a) y + 2y = x, y (0) = 1, Solution. Multiply by e2x to get (e2x y ) = xe2x and then integrate to get e2x y = x 2x 1 2x e e + C. 2 4 Solve for y and substit

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