s251ex1(su10) - y = 0 is unstable, y = 2 is semistable. (c)...

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MATH 251 Exam I July 6, 2010 ANSWER KEY 1. (a) 1, nonlinear (b) 2, linear (c) 2, nonlinear (d) 2, linear (PDE) 2. C 3. B 4. C 5. B 6. C 7. D 8. (a) t t c e C e C y - + = 2 4 1 (b) E (c) C (d) K 9. (a) μ ( t ) = e t / 2 (b) y = 3 t – 6 + Ce -t / 2 10. (a) t = time, Q ( t ) = the amount of salt in the tank at time t . (b) Q Q t - - = 50 6 50 , Q (0) = 0 11. (a) --- (b) y = ±2 is (asymptotically) stable,
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Unformatted text preview: y = 0 is unstable, y = 2 is semistable. (c) 2 12. y = C 1 t 2 + C 2 t 2 13. (a) T q = 3 2 (b) 12 > (c) none, it could not happen 14. (a) y ( t ) = C 1 e 2 t cos 3 t + C 2 e 2 t sin 3 t (b) y ( t ) = 2 e 2 t cos 3 t + e 2 t sin 3 t...
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This note was uploaded on 07/16/2011 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Pennsylvania State University, University Park.

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