s251ex1(sp03)

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online