MATH 3113 Midterm II - Solutions for Laplace Transforms and Differential Equations, Exams of Mathematics

Download MATH 3113 Midterm II - Solutions for Laplace Transforms and Differential Equations and more Exams Mathematics in PDF only on Docsity! MATH 3113 Midterm II November 14, 2008 Name : I.D. no. : • Calculators are not allowed. The problems are set so that you should not need calculators at all. • Show as much work as possible. Answers without explanation will not receive any credit. • Best of Luck. 1 i) a) (8 Points) Find L−1{ 4s + 7 s2 + 2s + 10 } b) (12 Points) Find the Laplace transform of the function f(t) given by the following graph. 2 iv) (15 Points) Find the Laplace transform of f(t) =  sin(t), if 0 ≤ t < 2π; 0, if 2π ≤ t < 4π; cos(t), if 4π ≤ t < 6π; 0, if 6π ≤ t. v) (10 Points) Find the singular points and guaranteed radius of convergence of a power series solution in powers of x− 1 of the differential equation (3 + x2)y′′ + (2x + 1)y′ + 4xy = 0. 5 vi) (20 Points) Find the recurrence relation and the first 3 non-zero terms of each of the 2 linearly independent power series solutions of the differential equation (2− x3)y′′ + x4y = 0. 6