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Unformatted text preview: takes a long way, as seen in question (a). 1 2. (30 points) Solve the initial value problem d y d x + 2 xy = x ex 2 , y (0) = 1 . 2 3. For d y d x = sin y cos y (a) (15 points) Sketch, roughly, a direction feld and classiy the critical points. (b) (10 points) Determine, rom your sketch, the asymptotic behavior o the solution or y (0) = 1 as t . 3 4. Solve the system 3 x 1 + x 2 + 2 x 3 = 4 x 2x 3 = 42 x 1 + 4 x 2x 3 = 11 using (a) (20 points) GaussJordan elimination, (b) (20 points) Cramers method. 4 5. Given the matrix A = 1 2 p1 3 31 P , (a) (15 points) compute A 2 and A 3 . (b) (15 points) Based on these results, determine the matrices A1 and A 2004 . 5...
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This note was uploaded on 08/11/2008 for the course MATH 475 taught by Professor Balazs during the Fall '05 term at Wisconsin.
 Fall '05
 BALAZS
 Math, Combinatorics

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