MTH 286 Midterm: MTH 286 Cleveland State Test2msol
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Test 2 di erential equations spring 2002, makeup due 4/22/02. Write your name on the back of your test. You must check your work to receive credit. 1. (14) for the di erential equation d2y dt2 + 4 dy dt. + 13y = sin 3t: compute the general solution, The general solution for the homogeneous problem is yh(t) = e 2t(k1 cos(3t) + k2 sin(3t)). We use complexi cation to nd a solution to the forced harmonic oscillator. For the problem d2y dt2 + 4 dy dt. + 13y = e3it, yc(t) = ae3it, c(t) = 3iae3it y c (t) = 9ae3it, y we guess a solution of the form then so ae3it( 9 + 12i + 13) = e3it. The problem we are interested in has a forcing function of sin 3t, but by euler"s formula, this is just the imaginary part of e3it, so our particular solution to the original problem is yp(t) = im{yc(t)} = im{
