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Math Help - Need Help Using Complex Exponentials To Solve Differential Equation

  1. #1
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    Need Help Using Complex Exponentials To Solve Differential Equation

    Hi,

    Can someone help me with the following?

    Use complex exponentials to find the solution of the differential equation

    ((d^2)y(t)/d(t^2)) + (3dy(t)/dt) + (25/4)y(t) = 0

    such that y(0) = 0 and dy/dt = 1 for t = 0.

    Thanks in advance
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  2. #2
    Eater of Worlds
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    Use your auxiliary equations to find the roots of the quadratic:

    m^{2}+2m+\frac{25}{4}=0

    m=\frac{-3}{2}+2i, \;\ m=\frac{-3}{2}-2i

    Now, you have:

    y=C_{1}e^{\frac{-3}{2}t}cos(2t)+C_{2}e^{\frac{-3}{2}t}sin(2t)

    Now, use your initial condtions to find C1 and C2.
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