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s251ex1(fa03)

# s251ex1(fa03) - (d lim t →∞ y t =-3 8(a Q t =...

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MATH 251 Fall 2003 Exam 1 October 14, 2003 ANSWERS: 1. First order, linear; Second order, linear; First order, nonlinear; Third order, nonlinear. 2. C 3. A 4. D 5. y ( t ) = - 4 + p x 4 - 3 x 2 + 3 x + 3 . 6. (a) ∂y (2 x + ye xy ) = e xy + xye xy = ∂x ( xe xy + 1) (b) x 2 + e xy + y = 2 7. (a) Equilibrium solutions are y = - 3 , y = 0 , and y = 2 . (b) y = - 3 is unstable, y = 0 is (asymptotically) stable, y = 2 is unstable. (c) lim t →∞ y ( t ) = 0
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Unformatted text preview: (d) lim t →∞ y ( t ) =-3 8. (a) Q ( t ) = 25000-20000 e-1 100 t (b) The limiting concentration is lim t →∞ Q ( t ) 500 = 25000 500 = 50 ( g m 3 ) , which is the same as the concentration of the in±ow. 9. y ( t ) = 2 e 3 t-te 3 t 10. y ( t ) = C 1 t + C 2 t 4...
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