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Math Help - Trial Solution for this Differential Equation

  1. #1
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    Trial Solution for this Differential Equation

    I'm having trouble figuring out the trial solution for this particular differential equation:

    y'' + 9y = (x^2)* sin x

    I wrote the trial solution as being (Ax^2 + Bx + C)(D cos x + E sin x)

    However my book writes it as being

    (Ax^2 + Bx + C)cos x + (Ex^2 + Fx + G) sin x

    Can someone explain to me why this is?
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  2. #2
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    Quote Originally Posted by zerobladex View Post
    I'm having trouble figuring out the trial solution for this particular differential equation:

    y'' + 9y = (x^2)* sin x

    I wrote the trial solution as being (Ax^2 + Bx + C)(D cos x + E sin x)

    However my book writes it as being

    (Ax^2 + Bx + C)cos x + (Ex^2 + Fx + G) sin x

    Can someone explain to me why this is?
    They are equivalent.
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