# S251ex1(fa07) - Y = A e 2 t B t 2 C t D E cos 2 t F sin 2 t(c Y = A t e 2 t cos 2 t B t e 2 t sin 2 t C(d Y = A t 2 B t C e-t cos 5 t D t 2 E t F

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MATH 251 Exam I October 4, 2007 ANSWER KEY 1. C 2. D 3. D 4. C 5. C 6. A 7. (a) y = 0, 5, 10 (b) y = 0 is (asymptotically) stable, y = 5 is unstable, and y = 10 is (asymptotically) stable. (c) 10 ) ( lim = t y t (d) y (21) = 10 8. (a) α = 2 (b) x 5 y 2 + e xy - 4 y = -19 9. (a) y ( t ) = 6 e t - e 6 t (b) -∞ = ) ( lim t y t 10. (a) t e C t e C y t t c 2 sin 2 cos 2 2 2 1 + = (b)

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Unformatted text preview: Y = A e 2 t + B t 2 + C t + D + E cos 2 t + F sin 2 t (c) Y = A t e 2 t cos 2 t + B t e 2 t sin 2 t + C (d) Y = ( A t 2 + B t + C ) e-t cos 5 t + ( D t 2 + E t + F ) e-t sin 5 t 11. 4 17 4 1 2 1 ) ( 2 2 +--= t t e te t y 12. y ( t ) = C 1 t 3 + C 2 t-1...
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## This note was uploaded on 07/23/2008 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Pennsylvania State University, University Park.

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S251ex1(fa07) - Y = A e 2 t B t 2 C t D E cos 2 t F sin 2 t(c Y = A t e 2 t cos 2 t B t e 2 t sin 2 t C(d Y = A t 2 B t C e-t cos 5 t D t 2 E t F

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