MTH 286 Midterm: MTH 286 Cleveland State Test2S03sol
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Test 2 di erential equations spring 2003, april 7-8, solutions. Write your name on the back of your test. 1. (25) for the di erential equation d2y dt2 + 10y = 2 cos 3t: compute the general solution, 2 + 10 = 0 yh(t) = k1 cos 10t + k2 sin 10t. Next, we use complexi cation to nd a solution to the particular problem: d2y dt2 + 10y = 2e3it yc(t) = ae3it y c(t) = 3iae3it y c (t) = 9ae3it. The general solution is y(t) = yp(t) + yh(t) 4 0. 4903784750: use the information from part b) to provide a rough sketch of a typical solution. 4 0. 01291364587, and the rapid oscillations have frequency. Solution: the sketch is omitted, but the period of the beats is oscillations it is. 2. (25) for the di erential equation d2y dt2 + 4 dy dt. + 3y = e 2t + 3: compute the general solution,
