This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MAT 514, Spring 2006 Introduction to Ordinary Differential Equations Final Exam Friday, May 5 You have 120 minutes to work the following 7 problems (10 pages). Correct answers without complete steps will not give full credit. Show ALL your work. Write all your solutions in clear, logical steps. Good luck! Your Name: Problem 1. (lOp.) Solve the initial value problem ty' + 2y  4t 2 = 0, y(l) = 2 and describe the behavior of the solution as t + 00. Problem 2. (3+7+5=15p.) (a) Show that the differential equation (2x  y) dx + (2y  x) dy == 0 is exact. (b) Solve the initial value problem (2x  y) dx + (2y  x) dy == 0, y(l) = 3. (c) Determine the interval in which the solution is valid. Problem 3. (lOp.) Find the solution of the initial value problem v" + 5y' + 6y = 0, y(O) = 2, y'(O) = 3 and describe the behavior of the solutions as t increases. Problem 4. (S+lO==lSp.) (a) Find the general solution of the differential equation y" + 4y == O. == O....
View
Full
Document
This note was uploaded on 01/15/2012 for the course MAT 514 taught by Professor Staff during the Fall '08 term at Syracuse.
 Fall '08
 Staff

Click to edit the document details