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s251ex1(su08)

s251ex1(su08) - MATH 251 Exam I July 8 2008 ANSWER KEY 1 C...

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Unformatted text preview: MATH 251 Exam I July 8, 2008 ANSWER KEY 1. C 2. C 3. B 4. D 5. y (t ) = −2 − 2 x 3 + 2 cos x + 2 6. (a) Q ′ = 20 − 2 Q, 80 − t Q(0) = 0 1 1 (b) Q(t ) = 20(80 − t ) − (80 − t ) 2 = 20t − t 2 4 4 7. (a) y = −2, 4.5, 8 (b) y = −2 is unstable, y = 4.5 is (asymptotically) stable, and y = 8 is unstable. (c) lim y (t ) = 4.5 t →∞ (d) lim y (t ) = 8 t →∞ 8. (a) ∂M ∂N = π cos(π x) + 3 x 2 = ∂x ∂y (b) y sin(πx) + x3y − 2e x + 5y = −13 − 2e 2 9. (a) y(t) = 3e 4t − 2 t e 4t (b) lim y (t ) = −∞ t →∞ 10. y(t) = C1 t 2 + C2 t 2 ln(t) 11. (a) y c = C1 e − t + C 2 e 2t (b) Y = 3 9 cos 2t − sin 2t 20 20 (c) Y = (A t 4 + B t 3 + C t 2 + D t) e −t + E e 2t cos 6t + F e 2t sin 6t ...
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s251ex1(su08) - MATH 251 Exam I July 8 2008 ANSWER KEY 1 C...

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