m3354_f05_q5_sol

m3354_f05_q5_sol - y = 2 cos(2 t ) 3. Find the general...

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Math 3354 Sec. 2, Quiz # 5 Name KEY 1. 2. Solve the initial value problem y 00 + 4 y = 0 with y (0) = 2 and y 0 (0) = 0. r 2 + 4 = 0 r = 0 ± 2 i . y = C 1 cos(2 t ) + C 2 sin(2 t ) 2 = y (0) = C 1 and since y 0 = - 2 C 1 sin(2 t ) + 2 C 2 cos(2 t ) 0 = y 0 (0) = 2 C 2 so we have
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Unformatted text preview: y = 2 cos(2 t ) 3. Find the general solution y 00 + 12 y + 36 y = 0. r 2 + 12 r + 36 = 0 ( r + 6) 2 = 0 r =-6 ,-6. y = C 1 e-6 t + C 2 te-6 t...
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