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Math Help - Differential Equation

  1. #1
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    Differential Equation

    Observe that is a solution, for any real c, of y'=2ty. Determine c so that y(0) = 2.

    Does anyone know how to solve this problem?Any help would be greatly appreciated, I'm pretty lost.
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  2. #2
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    Quote Originally Posted by cdlegendary View Post
    Observe that is a solution, for any real c, of y'=2ty. Determine c so that y(0) = 2.

    Does anyone know how to solve this problem?Any help would be greatly appreciated, I'm pretty lost.
    Here you are being asked to find c in y=ce^{t^2} given the initial condition y(0) = 2

    All you need to do is make y=ce^{t^2} into 2=ce^{0^2} as per the initial condition.

    Now solve 2=ce^{0^2} for c

    2=ce^{0^2}

    2=ce^{0}

    2=c\times 1

    c = 2
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