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TEXAS A&M UNIVERSITY DEPARTMENT OF MATHEMATICS MATH 308-502 Exam 2 version A, 25 Oct 2013 On my honor, as an Aggie, I have neither given nor received unauthorized aid on this work. Name (print): In all questions no analytical work =⇒ no points! 1. Solve the initial value problem y 00 + 5y 0 + 6y = e−3t , y(0) = 1, y 0 (0) = 0. 2. Find the general solution to y 00 + 9y = 1 . cos(3t) 3. Solve the initial value problem y 00 + 4y = sin(3t), y(0) = 0, y 0 (0) = 1. In view of Question 5, it is recommended to use the Laplace Transform method here. 4. The voltage E(t) supplied to a curcuit is sin(3t) for time 0 ≤ t ≤ π and is swithed off after time t = π. Express E(t) using the Heaviside function uc (t). Calculate the Laplace transform of E(t). 5. Solve the initial value problem y 00 + 4y = E(t), y(0) = 0, y 0 (0) = 0, where E(t) is given in question 4. Points: /25