MATH 202 Midterm, Summer 2011

Math 202 - Midterm (Summer 11) T. Tlas ================================================ • All questions have extra sheets for you to write your answers on them. Any part of your answers written on the wrong page will not be graded. • There are 3 problems in total. Some questions have several parts to them. Make sure that you attempt them all. • This is a closed book exam and no calculators are allowed. • The exam is out of 40. ================================================ Name : ID # : ================================================ Q1 Q2 Q3 TOTAL Problem 1 (5 points each) Solve the following IVPs: i- y′ = y2cos(x) ; y(0) = 1 ii- y′ = − 2xy x2 + cos(y) ; y(0) = 0 iii- y′ = 1 sin(x + 2y) − 1 2 ; y(0) = 0 ================================================ ADDITIONAL SHEET FOR PROBLEM 1 ANSWER Problem 2 (14 points) Solve the IVP y′′ + xy′ + y = 0 ; y(0) = 1 , y′(0) = 0 Also, find y(2). Hint: One of the series that you’ll obtain cannot be written in closed form, but this won’t be needed anywhere in this question. ================================================ ADDITIONAL SHEET FOR PROBLEM 2 ANSWER Problem 3 Solve the following IVPs: i- (3 points) x2y′′ + xy′ + 4y = 0 ; y(1) = 1 , y′(1) = 0 ii- (8 points) y′′′ − 2y′′ + y′ = ex ; y(0) = 0 , y′(0) = 0 , y′′(0) = 0 ================================================ ADDITIONAL SHEET FOR PROBLEM 3 ANSWER ================================================