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Math Help - Ordinary 2nd Ordinary Non-homogenous DE

  1. #1
    Member zangestu888's Avatar
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    Ordinary 2nd Ordinary Non-homogenous DE

    I wuould please like some verifcation on my work i think am on the write track, the question itself is

    y''-4y=3e^(2x)+12x-2

    For my homogeneous left side equation i have yh(x)=c1e^2x+c2e^-2x

    My particular guess for the right side was: ae^2x + bx + c (and since e^2x appears both in the homo and the right side i multiply by x so i have )

    axe^2x+bx+c as my guess doing the deritive and equating like terms i get,
    a=4/3, b=-3,c=1/4
    ? am not sure if these are my correct coeffcients any help will be appreciated! thanks!
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  2. #2
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    Quote Originally Posted by zangestu888 View Post
    I wuould please like some verifcation on my work i think am on the write track, the question itself is

    y''-4y=3e^(2x)+12x-2

    For my homogeneous left side equation i have yh(x)=c1e^2x+c2e^-2x

    My particular guess for the right side was: ae^2x + bx + c (and since e^2x appears both in the homo and the right side i multiply by x so i have )

    axe^2x+bx+c as my guess doing the deritive and equating like terms i get,
    a=4/3, b=-3,c=1/4
    ? am not sure if these are my correct coeffcients any help will be appreciated! thanks!
    Have you substituted your proposed solution into the differential equation to see if it works?
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  3. #3
    Member zangestu888's Avatar
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    um yes i have a get a werid result thats why i posted the thread becuase i think thier might be some sort of error?
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  4. #4
    MHF Contributor

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    Quote Originally Posted by zangestu888 View Post
    I wuould please like some verifcation on my work i think am on the write track, the question itself is

    y''-4y=3e^(2x)+12x-2

    For my homogeneous left side equation i have yh(x)=c1e^2x+c2e^-2x

    My particular guess for the right side was: ae^2x + bx + c (and since e^2x appears both in the homo and the right side i multiply by x so i have )

    axe^2x+bx+c as my guess doing the deritive and equating like terms i get,
    a=4/3, b=-3,c=1/4
    ? am not sure if these are my correct coeffcients any help will be appreciated! thanks!
    Show HOW you got those numbers and we will try to help.
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  5. #5
    Member zangestu888's Avatar
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    well i dereived my particular solution two times then subbed it into my differential equation when i equated terms i got those numbers but am not sure if my answr is correct i followed all procedures, am using method of undetermined coefficients

    I did this..

    yp(x)=axe^2x+bx+c i took the dervtive twice then i substtuted it into the de i got

    (4ae^2x+4axe^2x)-4(axe^2x+bx+c)=r(x)
    4ae^2x-4bx-4c=3e^2x+12x-2
    a=3/4,b=-3,c=1/2

    my final equation for the whole DE is...

    y(x)=2e^x2+2e^-2x+3/4(x)e^2x-3x=1/2
    Last edited by mr fantastic; June 16th 2009 at 07:56 PM. Reason: Merged posts
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