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Math Help - non-homogeneous equation

  1. #1
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    non-homogeneous equation

    1.) (D^2+1)=cosx

    2.) y"-3y'-4y=16x-50cos2x
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by alderon View Post
    1.) (D^2+1)=cosx

    2.) y"-3y'-4y=16x-50cos2x
    The general solutions to these take the form of the general solution to the corresponding homogeneous equation plus a particular integral of the non homogeneous equation.

    I will presume that you know how to solve the homogeneous equations y''+y=0 (which is what I presume your first equation id supposed to be) and y''-3y'-4y=0

    For the first, as \cos(x) is a solution of the homogeneous equation we try a trial solution (Ax+B)\cos(x) + (Cx+D)\sin(x)

    For the second we try a trial solution of the form (A x+ B) + C \cos(2x)+D \sin(2x)

    RonL
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