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MATH 4027  Ordinary Differential Equations  LSU Study Resources

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

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

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

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

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_(

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

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

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

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

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 (

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

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

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

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

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

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

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

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

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

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

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: 5781601 Email: adkins@math.lsu.edu Class Web Site: http:/www.math.lsu.edu/~adkins/m4027.html Office Hours: 9:40  10:30 A.M. M

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