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Math Help - homogeneous ODE

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    homogeneous ODE

    Anyone have any idea on how to work this question?

    Find the general solution of the homogeneous ODE
    \frac{d^2u}{dt^2} + 2\frac{du}{dt} + 5u= 0
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    Quote Originally Posted by mongmong View Post
    Anyone have any idea on how to work this question?

    Find the general solution of the homogeneous ODE
    \frac{d^2u}{dt^2} + 2\frac{du}{dt} + 5u= 0
    What do your class notes and/or textbook say about this type of differential equation?
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    Quote Originally Posted by mongmong View Post
    Anyone have any idea on how to work this question?

    Find the general solution of the homogeneous ODE
    \frac{d^2u}{dt^2} + 2\frac{du}{dt} + 5u= 0
    The Characteristic Equation is

    m^2 + 2m + 5 = 0

    You should find that in this case the solutions to the Characteristic Equation, m_1 = a + ib, m_2 = a - ib are complex conjugates.
    So the solution to your DE will be of the form

    u(t) = Ae^{at}\cos{(b t)} + Be^{at}\sin{(b t)}


    Hopefully you can go from here.
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