X1 2 y x 152 22 y x1 21 y find the particular

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Unformatted text preview: x 2 /2 , 2 y = 0. x+1 2 y = (x + 1)5/2 . 22. y + x+1 21. y + Find the particular solution determined by the initial condition. 23. y + y = x, 24. y − y = e , 2x 1 1 + y = y ; y1 (x) = x , y2 ( x ) = , e +1 C ex + 1 + 4y = 0; y1 (x) = 2 sin 2x, y2 (x) = 2 cos x. − 4y = 0; y1 (x) = e2x , y2 (x) = C sinh 2x, − 2y − 3y = 7e3x ; y1 (x) = e−x + 2e3x , y2 (x) = 7 xe3x . 4 8. xy − 2y = −x. 10. y − y = −2 e−x . cos x 12. xy + 2y = . x 14. y + y = 2 + 2x. 16. y − y = ex . y(0) = 1. y(1) = 1. Find the general solution. 7. y − 2y = 1. 9. 2y + 5y = 2. 11. y − 2y = 1 − 2x. 13. xy − 4y = −2nx. 15. y − ex y = 0. 17. (1 + ex ) y + y = 1. 18. xy + y = (1 + x) ex . 19. y + 2xy = x e−x . 2 1 , y(0) = e. 1 + ex 1 26. y + y = , y(0) = e. 1 + 2 ex 25. y + y = 27. xy − 2y = x3 ex , 28. xy + 2y = x e , −x y(1) = 0. y(1) = −1. 20. xy − y = 2x ln x. 29. Find all functions that satisfy the differential equation y − y = y − y . HINT: Set z = y − y. 30. Find the general solution of y + ry = 0 on [0, ∞) where r is a constant. (a)...
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This note was uploaded on 10/12/2010 for the course MATH 12345 taught by Professor Smith during the Spring '10 term at University of Houston - Downtown.

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