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Math Help - hyperbolic sin/cos differential equation

  1. #1
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    hyperbolic sin/cos differential equation

    Problem: Show that any function of the form:
    x = C_{1}\text{cosh}(\omega*t) + C_{2}\text{sinh}(\omega*t)
    satisfies the differential equation:
    x'' - \omega^2x = 0

    For x'' I have:
    x'' = C_{1}\text{cosh}(\omega*t) + C_{2}\text{sinh}(\omega*t)

    so...
    C_{1}\text{cosh}(\omega*t) + C_{2}\text{sinh}(\omega*t) - \omega^2[C_{1}\text{cosh}(\omega*t) + C_{2}\text{sinh}(\omega*t)] = 0

    where do I go from here?
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  2. #2
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    Quote Originally Posted by sgcb View Post
    Problem: Show that any function of the form:

    For x'' I have:
    x'' = C_{1}\text{cosh}(\omega*t) + C_{2}\text{sinh}(\omega*t)
    where do I go from here?
    This is wrong. By chain rule, each time you take derivative with respect to t, you'll get one more factor of \omega and so

    x'' = \omega^2 x
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