In Exercises 1-3use the Laplace transform to solve the inthal value problem. 1, y'(0) = -1 y(0) = 1 1. y +3y+2ye', y(0) 1, y(0) --6 3. "+y-2y=2e, y(0)=-1, y(0) = 4 5. yy 2ye", y(0) = 7. yysin 2. y(0) = 0, 9. y" -3y+2ye, y(0) 1, y(0) = -2 11. y +3y+2y=2e'. y(0) = 0, y(0) --1 13. y+4y4, y(0) = 0, y'(0) = 1 15. y" + 3y+2y=e', y(0) = 0, y(0) = 1 17. y" + 4y 3 sint, y(0) = 1, y'(0) = -1 19. yyl, y(0) 2, y(0) = 0 == 2. y"-y-6y=2, y(0) = 1, y(0) = 0 4. y4y2e, y(0) = 1, y'(0) = -1 6. y+3y+2y=6', y(0) - 1. y(0) = -1 8. y"-3y+2y=2e, y(0) 1, y(0) - 1 - 10. y 3y+2y=g, y(0)=-1, y(0) -4 12. y+y-2y=-4, y(0) = 2, y(0) = 3 14. yy'-6y=2, y(0) = 1, y'(0) = 0 16. yy 1, y(0) 1, y(0) 0 18. yy 28, y(0)-1, y(0) = 4 20. yy, y(0) = 0, y(0) 2 22. y" + 5y' +6y=2e ", 1, y'(0) = -3 y(0) 4 cost, y(0)-1, y(0) - 1 21. yy 3 sin 2t, 23. y" + 2y + y6 sin 24. y" -2y-3y=10 cost, y(0) = 2, y'(0) = 7 1 25 y+y4 sint + 6 cost, y(0)=-6, y'(0) - 2 26. y + 4y 8 sin 2t+9 cost, y(0) = 1, y(0) 0 27y5y+6y 10e' cost, y(0) = 2, y(0) 28y" + 2y + 2y = 21, y(0) = 2, y(0) = -+ 29. y2y+2y-5 sin+10 cost, y(0) 1, 30. y +4y+13y =10e36e, y(0) = 0, 31. y" +4y+Sy e(cos +3 sin ), y(0) = 0, y(0) -4 F '(0) = 2. y(0) = -16 32. 2y" 3y-2y=4e', y(0) 1, y'(0) = -2 33. 6yyy 3e, y(0) = 0, y'(0) = 0. 34. 2y" +2y+y2t. y(0) 1, y(0) = -1 35. 4y4y+5y 4 sin(-4 cost, y(0) = 0, y'(0) = 1. 36. 4y+4y+y=3 sin+cost, y(0)=2. y'(0) = -1 37. 9y" +6y+y 3e, y(0) = 0, y'(0) = -3 y(0) = 1, y(0) 3 *