This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 classi±y 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) Cramer’s 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...
View
Full Document
 Fall '05
 BALAZS
 Math, Combinatorics, Acceleration, Velocity, Tram, Electric vehicle

Click to edit the document details