3354_f05_t2sol

3354_f05_t2sol - Math 3354 , Test # 2, Name KEY 1. Use the...

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Unformatted text preview: Math 3354 , Test # 2, Name KEY 1. Use the substitution y = x reduce to first order and solve tx = 2x . ANSWER: c1 + c2 t3 2. Solve the initial value problem y − 9y = 0 y (0) = 2, y (0) = 0. ANSWER: e3t + e−3t 3. Find the general solution y + 4y + 29y = 0. ANSWER: y = c1 e−2t sin(5t) + c2 e−2t cos(5t) 4. Find the general solution of t2 y + 5ty + 4y = 0 (Answer must be in t). ANSWER: y = c1 t−2 + c2 t−2 ln(t) 5. Find the general solution of y + y + 4y + 4y = 0. ANSWER: y = c1 e−t + (c2 sin(2t) + c3 t) cos(2t) 6. Find the form of a particular solution yp (t) for y − y = t sin(t) + 2t. (DO NOT SOLVE FOR CONSTANTS) ANSWER: y = (At + B ) cos(t) + (Ct + D) sin(t) + t(Et + F ) 7. Use undetermined coefficients to find a particular solution for y − y = 2e−t . ANSWER: yp = −te−t 8. Use variation of parameters to find a particular solution for y − y = 6e2t . ANSWER: yp = 3e2t ...
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