MATH 202 Exam 2, Fall 2013

Math 202 - Quiz 2 (Fall 13) T. Tlas ================================================ • Write the answer to question 3 on its sheet. 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. Remember that a sheet is two pages/faces. • There are 3 problems in total. The first question has several parts to it. Make sure that you attempt them all. • This is a closed book exam and no calculators are allowed. ================================================ Name : ID # : Section : ================================================ Q1 Q2 Q3 TOTAL Problem 1 (15 points each) Find y(t) in each of the following problems: i- ¨y + 4y = 1 − U(t − 1) ; y(0) = 0 , ˙y(0) = −1 ii- ˙y + y = δ(t − 1) ; y(0) = 2 iii- t − 2y(t) = � t 0 (eτ − e−τ)y(t − τ)dτ ================================================ ADDITIONAL SHEET FOR PROBLEM 1 ANSWER ADDITIONAL SHEET FOR PROBLEM 1 ANSWER Problem 2 (45 points) Solve the following BVP: y′′ + 2 xy′ + y = 0 ; y(0) = 1 , y(π) = 0 Also find y(1000). Hint : Solve around 0. ================================================ ADDITIONAL SHEET FOR PROBLEM 2 ANSWER ADDITIONAL SHEET FOR PROBLEM 2 ANSWER Problem 3 (10 points) Assume the following equations are satisfied: ∞ � n=0 anxn = ex2 ∞ � n=0 bnxn = sin(x3) ∞ � n=0 cnxn = y(x) cn = n � k=0 akbn−k. Then y(10) = ? ================================================