MATH 202 Exam 2, Fall 2011

Math 202 - Quiz 2 (Fall 2011) T. Tlas ================================================ • Write the answer to questions 3 and 4 on their corresponding sheets. The first two questions have extra sheets for you to write your answers on them. Any part of your answers written on the wrong sheet will not be graded. • There are 4 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. ================================================ Name : ID # : Section : ================================================ Q1 Q2 Q3 Q4 TOTAL Problem 1 (30 points) Solve the following IVP: y′′ − 3x2y′ − 6xy = 0 ; y(0) = 1 , y′(0) = 0 Also, find y(2). ================================================ ADDITIONAL SHEET FOR PROBLEM 1 ANSWER ADDITIONAL SHEET FOR PROBLEM 1 ANSWER Problem 2 Solve the following equations/system of equations: i- (15 points) y = t3 6 + 1 6 � t 0 (t − τ)3y(τ)dτ ; y(0) = 0 ii- (15 points) ¨y − 7 ˙y + 6y = δ(t − 2) ; y(0) = 0 , y′(0) = 0 iii- (20 points) ˙x − x − y = δ(t − 1) ˙y + y + x = U(t − 1) ; x(0) = 0 , y(0) = 0 ================================================ ADDITIONAL SHEET FOR PROBLEM 2 ANSWER ADDITIONAL SHEET FOR PROBLEM 2 ANSWER Problem 3 (10 points) Solve the following BVP: x2y′′ + xy′ + (x2 − 1 4)y = 0 ; y(π 2 ) = 2 π , y(π) = 0 Hint: J 1 2(x) = � 2 πx sin(x) and J− 1 2 (x) = � 2 πx cos(x) ================================================ Problem 4 (10 points) If y(x) solves the IVP below, find y(2): y′ = 2x � � � �1 − x4 � ∞ � n=0 (−1)n x4n (2n + 1)! �2 ; y(0) = 0 ================================================