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Texas A&M University Department of Mathematics Volodymyr Nekrashevych Fall 2011 MATH 308 Homework 5 5.1. Find the solution of the initial value problem y 00 − 2y 0 + y = tet + 4, y(0) = 1, y 0 (0) = 1. Plot it using MatLab. (Try to choose a nice interval [0, T ] on which to plot the graph.) 5.2. Find the general solution of the differential equation y 00 + 4y 0 + 4y = t−2 e−2t , t > 0. 5.3. A mass weighing 2 lb stretches a spring 6 in. If the mass is pulled down an additional 3 in. and then released, and if there is no damping, determine the position u of the mass at any time t. Find the frequency, period, and amplitude of the motion. 5.4. A mass weighing 4 lb stretches a spring 1.5 in. The mass is displaced 2 in. in the positive direction from its equilibrium position and released with no initial velocity. Assuming that there is no damping and that the mass is acted on by an external force of 2 cos 3t lb, formulate the initial value problem describing the motion of the mass. 5.5. Use integration by parts to find the Laplace transform of f (t) = t sin at.