MATH 246 Midterm: MATH246 ALL-SECTIONS SUMMER II2006 0000 MID EXAM 2

• School: University of Maryland
• Department: Mathematics
• Course: MATH 246
• Professor: All

Document Summary

Write down any formula that you use but don"t derive. Show all your work on these pages, using the backs for scratch paper. 1 s2 + 9(cid:19) (b) s + 2 s2 + 2s + 2 (c) e 2s s2 s. Math 246: (20 points) do not solve for y, simply nd the laplace transform, l(y)(s) = F (s). y + 2y + 2y = e t where y(0) = 1, y (0) = 2: (30 points) for each of the following matrices a, nd the eigenvalues and the corresponding eigenvectors. (a) (cid:18) 1. Math 246: (25 points) solve the following initial value problem: x = 3x 2y y = 4x + y where x(0) = 1, y(0) = 1. 2(cid:19) ; r = 3, v = (cid:18) 3. 2(cid:19) . (b) r = 4, v = (cid:18) 0. 1(cid:19) ; r = 2, v = (cid:18) 3. 5(cid:19) . (c) r = 2 i, v = (cid:18) 1 i.