s251ex1(su06) - 2 x 3-x 2 y e x y = 4 9 y t = 3 e-2 t cos 3...

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MATH 251 Summer 2006 Exam I June 29, 2006 ANSWERS: 1. (a) Third order, linear; (b) First order, nonlinear; (c) Second order, nonlinear. 2. C 3. C 4. B 5. A 6. (a) y ( t ) = t 2 sin t + 2 π 2 t 2 ; (b) (0 , ) . 7. (a) y = 6 , 5 , - 5 ; (b) y = - 5 is (asymptotically) stable, y = 5 is unstable, y = 6 is semistable; (c) lim t →∞ y ( t ) = - 5 ; (d) y 0 = 5 . 8. (a) ∂M ∂y = - 2 x + e x + y = ∂N ∂x
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Unformatted text preview: 2 x 3-x 2 y + e x + y = 4 . 9. y ( t ) = 3 e-2 t cos 3 t-e-2 t sin 3 t 10. y ( t ) = C 1 t + C 2 t ln t 11. (a) Q = 100-1 200 Q, Q (0) = 0 ; (b) Q ( t ) = 20000-20000 e-t 200 ; (c) t = 200 ln 2 ; (d) lim t →∞ Q ( t ) = 20000 g ....
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