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    Differential Equations and Variation of Parameters

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    Solve t^2y''+ty'-y=2t^2 sin t t not equal to zero

    Use method of variation of parameters
    Solve ∫t^2 sin t dt= -t^2 cos t + 2t sin t +2 cos t

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    The solution is attached below in two formats. one is in Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

    I assume we could use the integral you provided as is.

    To solve

    One must first solve the associated homogenous equation

    This equation can be solved using a "guess":

    Substituting ...

    Solution Summary

    An ODE and an integral are solved. The solution is detailed and well presented.