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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 =∞→tyt (d) y(21) = 10 8. (a) α = 2 (b) x5y2+ e xy − 4y = −19 9. (a) y(t) = 6e t − e 6t (b) −∞=∞→)(lim tyt 10. (a) teCteCyttc2sin2cos2221+= (b) Y = A e 2t + B t 2 + C t + D + E cos 2t + F sin 2t (c) Y = A t e 2t cos 2t + B t e 2t sin 2t + C (d) Y = (A t 2 + B t + C) e −t cos 5t + (D t 2 + E t + F) e −t sin 5t11. 4174121)(22+−−=ttetety 12. y(t) = C1 t 3 + C2 t
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