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Math Help - Differential equations - undetermined coefficients

  1. #1
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    Feb 2009
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    Differential equations - undetermined coefficients

    Hey guys!
    I have a quiz tomorrow and i'm not going to be able to sleep unless I understand the solution to this question. it's long, I kinda feel bad even asking

    Anyway the question is:

    Use method of undetermined coefficients to find the particular solution to

    y''' - 3y'' + 4y = e^2x

    I took my yp = x^2 * Ae^2x
    I multipllied by x^2 because of the double roots ( I got 2,2,-1 for roots)

    Thanks so much to anyone who can help me... I know its a long one.
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  2. #2
    Junior Member
    Joined
    Mar 2008
    Posts
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    Quote Originally Posted by ubique View Post
    Hey guys!
    I have a quiz tomorrow and i'm not going to be able to sleep unless I understand the solution to this question. it's long, I kinda feel bad even asking

    Anyway the question is:

    Use method of undetermined coefficients to find the particular solution to

    y''' - 3y'' + 4y = e^2x

    I took my yp = x^2 * Ae^2x
    I multipllied by x^2 because of the double roots ( I got 2,2,-1 for roots)

    Thanks so much to anyone who can help me... I know its a long one.
    Hello ubique,

    You are doing the right thing. Just take the derivatives of this and substitute it in the DE. You will see that it gives you the value of A directly.

    p.e. the first derivative is:

    y'_p=2A(x+x^2)e^{2x}

    Let us know if this helps,

    Coomast
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