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Math Help - general solutions to the ODE

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    general solutions to the ODE

    I need to find a real general solution to y'' + 9y = 18x + 36 sin3x
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    Quote Originally Posted by snewman16 View Post
    I need to find a real general solution to y'' + 9y = 18x + 36 sin3x

    Where are you stuck?

    Can you solve y'' + 9y = 0?

    Can you find a particular solution to y'' + 9y = 18x ?

    To get a particular solution to y'' + 9y = 36 sin(3x) you will need to construct a particular solution of the form y = Ax [ sin(3x) + cos(3x) ]. Substitute and determine the value of A (tedious to be sure but not difficult).
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