SupplementaryHW

SupplementaryHW - MAP 2302 Differential Equations I...

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Unformatted text preview: MAP 2302 Differential Equations I Supplementary Homework Problems 2-2 Separation of variables Solve the following differential equations by separation of variables: 1. dy dx = cos3 x 2. dy + e 2 ydx = 0 3. ( x- 1) dy dx =- x + 1 4. x 2 y =- 2 y 5. dx dy = x 2 y 3 1 + x 6. dy dx = e x- 2 y 7. (1 + x 2 + y 2 + x 2 y 2 ) dy = y 2 dx 8. ( y ln x ) dx dy = y- 1 x 2 9. sec 2 xdy- csc ydx = 0 10. e y sin3 xdx + ( e 2 y + y )cos xdy = 0 11. dy dx = xy + 3 x- y- 3 xy- 2 x + 4 y- 8 12. dy dx = sin x (cos2 y- cos 2 y ) 13. x p 1- y 2 dx =- 2 dy 14. ( e x- e- x ) dy dx = y 2 Solve the following initial value problems: 15. ( e- y + 1)sin xdx = (1 + cos x ) dy, y (0) = 1 16. ydy = x ( y 2 + 1) 1 2 dx, y (0) = 1 17. dy dx + xy = y, y (1) = 0 18. dy dx = y 2- 1 x 2- 1 , y (2) = 2 1 2-3. The first-order linear differential equations Solve the following linear equations: 1. dy dx = 4 y 2. 2 dy dx- 10 y = 3 3. dy dx + y = e 2 x 4. y + x 2 y = x 2 5. ( x- 4 y 2 ) dy + 3 ydx = 0 6. 2 xdy = ( x cos x- y ) dx 7. x 3 y + xy = 1 8. (1 + e x ) dy dx + e x y = 0 9. sin x dy dx- y cos x = 1 . 10. x dy dx + 3 y = x 2- x 11. x 2 y- x ( x + 1) y = e x 12. ydx + ( x + 2 xy 2 + 2 y ) dy = 0 13. cos 2 x sin xdy + ( y cos 3 x- 1) dx = 0 Solve the following initial value problems: 14. y = 2 y + x ( e 2 x- e x ) , y (0) = 1 15. xdy + ( xy + 2 y- 2 e x ) dx = 0 , y (1) = 0 16. x ( x- 2) y + 2 y = 0 , y (2) = 2 17. sin x dy dx + y cos x = 0 , y - 2 = 1 18....
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SupplementaryHW - MAP 2302 Differential Equations I...

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