Exercises 11.4 Solve each differential equation. dy 5y=e dx 2. +3y=e-2 dx 3. dy + dx 3y x 5. y' + 2xy=ex (3 + 2x) 7. dy 4y dx = x²ex dx 9. x dy 5y dx = (x + 4x) dx 11. (1 + x2) dy + 2xy dx = 3x² dx 13 x²y' + 2xy = x - 7 dy 15. + 2y = ex dx dy 2y = x² + 5 4. dx x 6. y' - 3x2y=e(3x² - 1) 8. dy-3x²y dx = x² dx dy 10. x dx dy 12. dx - + 2y = (x² + 4)³ y tan x = sin x 14. x2 y2xy=x³ +5 16. (x + 1) dy dx +5y=10 dy y 18. + = 8 19. y' y cos x = cos x dx 3.x - 1 dy 17. x- - y = 3x² dx dy 20. + y sec² x = sec²x dx Find a particular solution of each differential equation subject to the given initial conditions. x²+3; y = 3 when x = 1 dy dy y 21. 3y =e; y = 2 when .x = 0 22. =x dx dx x dy 77 3TT 23. csc xy cot x; y = dx 2 = 2 24. dy =(x-3y) dx; y(0) = 1 26. y' +8x2y=4x²; y(0) = 2 25. y'ey; y(0) - dy 27. x- + y = 3; y(1)=-2 dx 29. xy' + y = 4x³; y(2) = 3 CHAPTER 11 First-Order Differential Equations dy 3y 28. = dx (x-4)²; y(5) = 3 x-4 30. y' + y sin x = sin x; y(w/2) = 3