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Math Help - Differenation/Differential Equation

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    Differenation/Differential Equation

    Hi, I'm lost with this question. Never done differential equations before, yet...

    From the equation y'' + y' - 2y = x^2, find constants A,B and C such that the function y = Ax2 + Bx + C satisfies the equation.
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    Quote Originally Posted by millerst View Post
    Hi, I'm lost with this question. Never done differential equations before, yet...

    From the equation y'' + y' - 2y = x^2, find constants A,B and C such that the function y = Ax2 + Bx + C satisfies the equation.
    y = Ax^2 + Bx + C<br />

    y' = 2Ax + B

    y'' = 2A

    y'' + y' - 2y = x^2

    2A + (2Ax + B) - 2(Ax^2 + Bx + C) = x^2

    -2Ax^2 + (2A-2B)x + (2A + B - 2C) = x^2

    match up the coefficients ...

    -2A = 1

    2A - 2B = 0

    2A + B - 2C = 0

    solve for A, B, and C.
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