This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: and uniqueness theorem? (d) Solve dx dt =-x t-2 . How many solutions satisfy x (2) = 1? (e) Why this does not violate the existence and uniqueness theorem? 3. (18 points) Find all real numbers such that (a) t is a solution of ( t 2 D 2-3 tD + 2) x = 0. (b) 2 + 2 t + t 2 is a solution of ( D-1) x = t 2 . Exam Continues on Other Side 1 4. (20 points) Solve x-x = e t sin t , x (0) = 1. 5. (20 points) (a) Compute det e t sin t cos t e t cos t-sin t e t-sin t-cos t (b) Use a) to show that c 1 e t + c 2 sin t + c 3 cos t is the general solution of ( D-1)( D 2 + 1) x = 0 6. (20 points) (a) Find the general solution of ( D 3-2 D 2 + D ) x = 0. (b) Find the solution for which x (0) = x (0) = 0, x 00 (0) = 1. End of Exam 2...
View Full Document