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Math Help - [SOLVED] inhomogenous 2nd order D.e hard!

  1. #1
    Member i_zz_y_ill's Avatar
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    [SOLVED] inhomogenous 2nd order D.e hard!

    Im not quite sure what trial particular integral to use for this equation \frac{d^2y}{dx^2}-3\frac{dy}{dx}+2y=2e^x-5e^(2x) I get the complementary function to be Ae^x+Be^(2x) Do i needto include a minus in my trial particular integral,,or an x^2? I wouldnt have thought i need a x^2 any ideas??
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  2. #2
    Senior Member Danneedshelp's Avatar
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    Not quite sure I know what you are asking.

    y"-3y'+2y=2e^{x}-5e

    Find the roots of the characteristic equation

    r^{2}-3r+2=0 so, r_{1}=1 and r_{2}=2

    Thus, the homogenous part of your equation is...

    y(t)=C_{1}e^{x}+C_{2}e^{2x}

    That looks like what you got. Is there more to the problem? Do you need to find the particular solution?
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  3. #3
    Member i_zz_y_ill's Avatar
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    yeah thats right i just cant find the right trial solution to use that gives me the correct answer any ideas?
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  4. #4
    Member i_zz_y_ill's Avatar
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    is this just a really hard question ,,my only problem is when originally there were two e^xs on the right hand side does the trial particular solution have to have two e^xs. The answer the book got was  y+Ae^x+Be^2x-2xe^x-5xe^2x
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  5. #5
    MHF Contributor Calculus26's Avatar
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    Its not clear what the rhs of your eqn is.

    Is it 2e^x -5e^(2x) ?

    In this case :

    i yp = Axe^x +B x e^(2x)

    As e^x and e^(2x) are complimentary solutions

    Similarly in the answer given do you mean - 5xe^(2x)

    which would be consistent with i.
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