m3354_f05_q7_sol

m3354_f05_q7_sol - Math 3354 Sec. 2, Quiz # 7 Name KEY 1....

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Unformatted text preview: Math 3354 Sec. 2, Quiz # 7 Name KEY 1. Use variation of parameters to find a particular solution y − 4y = 3et . y − 4y = 0 ⇒ λ2 − 4 = 0, ⇒ λ = ±2 ⇒ y1 = e2t , y2 = e−2t e2t e−2t 2t −2t ) − (2e2t e−2t ) = −4 W= 2t −2t = (−2e e 2e −2e e−2t 3et dt + e−2t −4 −3e−2t e dt + 4 −t yp = −e 2t e2t 3et dt −4 e3t dt 3e2t = 4 3e2t = 4 = −et e−t −1 −3e−2t + 4 e3t 3 2. Use variation of parameters to find a particular solution y = t. (Note y1 = 1 and y2 = t since λ2 = 0 ⇒ λ = 0, 0). W= 1t =1 01 1·t dt 1 = t3 11 − 23 yp = −1 =− t3 = 6 t3 3 t·t dt + t 1 +t t2 2 ...
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