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9.3.1: Solution of Initial Value Problems (Exercises)

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    In Exercises 1-35 use the Laplace transform to solve the initial value problem.

    1. \(y'-y=1, \quad y(0)=0\)

    2. \(2y'+y=0, \quad y(0)=-3\)

    3. \(y'+6y=e^{4t}, \quad y(0)=2\)

    4. \(y'-y=2\cos 5t, \quad y(0)=0\)

    5. \(y''+5y'+4y=0, \quad y(0)=1,\quad y'(0)=0\)

    6. \(y''-4y'=6e^{3t}-3e^{-t}, \quad y(0)=1,\quad y'(0)=-1\)

    7. \(y''+y=\sqrt2\sin\sqrt2 t, \quad y(0)=10,\quad y'(0)=0\)

    8. \(y''+9y=e^t, \quad y(0)=0,\quad y'(0)=0\)

    9. \(2y'''+3y''-3y'-2y=e^{-t}, \quad y(0)=0,\quad y'(0)=0, \quad y''(0)=1\)

    10. \(y'''+2y''-y'-2y=\sin 3t, \quad y(0)=0,\quad y'(0)=0, \quad y''(0)=1\)

    11. \(y''+3y'+2y=e^t, \quad y(0)=1,\quad y'(0)=-6\)

    12. \(y''-y'-6y=2, \quad y(0)=1,\quad y'(0)=0\)

    13. \(y''+y'-2y=2e^{3t}, \quad y(0)=-1,\quad y'(0)=4\)

    14. \(y''-4y=2 e^{3t}, \quad y(0)=1,\quad y'(0)=-1\)

    15. \(y''+y'-2y=e^{3t}, \quad y(0)=1,\quad y'(0)=-1\)

    16. \(y''+3y'+2y=6e^t, \quad y(0)=1,\quad y'(0)=-1\)

    17. \(y''+y=\sin2t, \quad y(0)=0,\quad y'(0)=1\)

    18. \(y''-3y'+2y=2e^{3t}, \quad y(0)=1,\quad y'(0)=-1\)

    19. \(y''-3y'+2y=e^{4t}, \quad y(0)=1,\quad y'(0)=-2\)

    20. \(y''-3y'+2y=e^{3t}, \quad y(0)=-1,\quad y'(0)=-4\)

    21. \(y''+3y'+2y=2e^t, \quad y(0)=0,\quad y'(0)=-1\)

    22. \(y''+y'-2y=-4, \quad y(0)=2,\quad y'(0)=3\)

    23. \(y''+4y=4, \quad y(0)=0,\quad y'(0)=1\)

    24. \(y''-y'-6y=2, \quad y(0)=1,\quad y'(0)=0\)

    25. \(y''+3y'+2y=e^t, \quad y(0)=0,\quad y'(0)=1\)

    26. \(y''-y=1, \quad y(0)=1,\quad y'(0)=0\)

    27. \(y''+4y=3\sin t, \quad y(0)=1,\quad y'(0)=-1\)

    28. \(y''+y'=2e^{3t}, \quad y(0)=-1,\quad y'(0)=4\)

    29. \(y''+y=1, \quad y(0)=2,\quad y'(0)=0\)

    30. \(y''+y=t, \quad y(0)=0,\quad y'(0)=2\)

    31. \(y''+y=t-3\sin2t, \quad y(0)=1,\quad y'(0)=-3\)

    32. \(y''+5y'+6y=2e^{-t}, \quad y(0)=1,\quad y'(0)=3\)

    33. \(y''-2y'-3y=10\cos t, \quad y(0)=2,\quad y'(0)=7\)

    34. \(2y''-3y'-2y=4e^t, \quad y(0)=1,\; y'(0)=-2\)

    35. \(6y''-y'-y=3e^{2t}, \quad y(0)=0,\; y'(0)=0\)

    This page titled 9.3.1: Solution of Initial Value Problems (Exercises) was last modified on Tue, 08 Nov 2022 02:45:35 GMT and is shared under a not declared license and was authored, remixed, and/or curated by William F. Trench.

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