MATH 251 Final: MATH 251 PSU s251Final(su03)
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A a d. e. that satis es these requirements is y = (y 1)(y 2)(y 3). B a d. e. that satis es these requirements is y + 4y + 4y = 3 cos t 4 sin t. C a d. e. that satis es these requirements is 2xy + ey + (x2 + xey) dx dy = 0. Q#:2 the answer, for both methods, is y(t) = t. A there is an equilibrium solution at v = 15, which is stable, and another at v = 15, which is unstable. B the solution is t + c = 1. 120 [ln(30 + 2v) ln(30 2v)]. A the d. e. is y + 7y + 10y = cos t u3 (t) cos t, with initial conditions y(0) = 0 and y (0) = 2. D the natural frequency is o = 10 rad. A the solution is x(t) = e t(cid:20) 5. B this critical point, the only one, is a stable node.
