MATH 202 Exam 1, Fall 2011

Math 202 - Quiz 1 (Fall 11) 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. • 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. ================================================ Name : ID # : Section : ================================================ Q1 Q2 Q3 TOTAL Problem 1 (15 points each) Solve the following IVPs: i- y′ = cos(x) yey ; y(0) = 1 ii- y′ = y x − exy2 ; y(1) = 2 iii- y′ = − y 2x + 2cos(y2) ; y(0) = 0 ================================================ ADDITIONAL SHEET FOR PROBLEM 1 ANSWER Problem 2 (15 points each) Solve the following IVPs: i- y′′′ − 4y′′ + 5y′ − 2y = 2sin(x) + 4cos(x) ; y(0) = 0 , y′(0) = 1 , y′′(0) = 1 ii- y′′ − 2yy′ = 0 ; y �π 2 � = 0 , y′�π 2 � = 1 iii- x2y′′ − 2xy′ + 2y = −x2 y(1) = 1 , y′(1) = 2 ================================================ ADDITIONAL SHEET FOR PROBLEM 2 ANSWER ADDITIONAL SHEET FOR PROBLEM 2 ANSWER Problem 3 (10 points) Assume that f(x, y) is a differentiable function of two variables with continuous partial derivatives which satisfies the following two equations: ∂f(x, y) ∂y = x f(x, y). f(x, 0) = 1 for all x. Find f(x, y). ================================================