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Math Help - Variation of Parameters

  1. #1
    Junior Member ihmth's Avatar
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    Variation of Parameters

    Using variation of parameters, solve for the general solution of:
     (D^2-2D+1)y = (e^2)^x((e^x+1)^-)^2

    I tried to solve for this several times but I keep getting the wrong answer, so I need help pls.

    -tnx
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  2. #2
    MHF Contributor Calculus26's Avatar
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    See attachment

    Note : in the attachment I wrote the soultion as

    c1e^(x) +c2xe^(x) +e^(x)[ln(e^x+1)-x]

    however the -x e^(x) can be absorbed into c2xe^(x) so it should read:

    y = c1e^x +c2xe^x + e^(x)ln(e^x+1)
    Attached Files Attached Files
    Last edited by Calculus26; August 7th 2009 at 09:02 AM.
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  3. #3
    Junior Member ihmth's Avatar
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    In my answer I keep getting an extra term "  -xe^x " and according in the book the answer is y = yc +  e^xln(1 + e^x) ...where yc is the complimentary solution. So it is possible for  -xe^x to be absorbed by one of the terms in the complementary solution...Now I know thank you
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  4. #4
    MHF Contributor Calculus26's Avatar
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    I edited my last post to make that exact point as at first I did the same thing
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