s251ex1(sp03) - 2 ) =-4 t , which is not equal to zero when...

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MATH 251 Spring 2003 Midterm Exam I 1. i. linear, order 2; ii. nonlinear, order 1; iii. linear, order 3; iv. nonlinear, order 2. 2. (a); 3. (c); 4. (c); 5. (d). 6. (a) equilibrium solutions: y = - 2 , 0 , 2 ; (b) y = - 2 asymptotically stable; y = 0 unstable; y = 2 asymptotically stable; (c) y ( t ) = 2 . 7. (a) Q ( t ) = - 6 e - t/ 200 + 6 ; (b) it will never happen (or, when t approaches infnity). 8. (b) x ln y + x 2 y + sin 2 x = C . 9. (a) yes; (b) yes: W ( y 1 , y
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Unformatted text preview: 2 ) =-4 t , which is not equal to zero when t is not zero; (c) since y 1 and y 2 are two linearly independent solutions, the general solution is thereFore y ( t ) = C 1 t 3 + C 2 t-1 . 10. (a) y ( t ) = C 1 e-4 t + C 2 e t ; (b) y ( t ) = C 1 e-4 t + C 2 e t-3 cos2 t-4 sin 2 t . 11. y ( t ) = 3 e-3 t + 8 te-3 t ....
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This note was uploaded on 07/23/2008 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Pennsylvania State University, University Park.

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