PROBLEMS: Section 3.7 For each differential equation in Problems 1-21, find the gen- eral solution by finding the homogeneous solution and a par- ticular solution. 1. y' = 2. y' + = 1 3. y' + y = x 4. y" = 1 5. y" + 4y = 1 6. y" 4y 1 7. y" + 4y = x 8. y" 9. y" 10. y" - 11. y" y2y = 3 - 6x y6e* + 3 y 2y = 6e* - y6 sin 2x 12. y"+4y' + 5y = 2e* 13. y" + 3y sin x + 2 cos x = 14. y" +4y' + 4y = xe¯* 15. y" yx sin x - - 16. y" 17. y” – 4y - - 18. y" 19. y" 20. y" - 3y' + 2y = e* sin x + 4y = xe y 12 cos² x = 4y' + 3y = y8xe* = 20 cos x 21. y" 5y + 6y = cosh x For Problems 22-28, find the solution to the initial-value prob- lem. 22. y' - y = 1 y(0) = 0 23. y" + y = 2x y(0) = 1 y' (0) = 2 24. y" + y2y = 2x y(0) = 0 y'(0) = 1 25. y" 5y' +6y=e* (2x-3) y(0) = 1 y' (0) = 3 - 26. y" 27. y" +16y= 5 sin x 28. y" + 3y' + 2y 4y' + 4y = e²x y(0) = 0 y' (0) = 0 y(0) = 0 y' (0) = 0 = 20 cos 2x y(0) = -1