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Second order linear differential equation, stuck on particular integral

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    The question is:
    General solution of
    d^2y/dx^2−4dydx+4y=2e^2x
    I have got the complementary function as (A+Bx)e2x=0 but when finding the Particular integral I substitute back I am getting zero? I have tried both y=Ce2xand Cxe2x ?

    I tried Cx^2e^2x because I realised it needs to be independent of the homogeneous equation but then I get two variables C and x to solve in the end?
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    Sorry, don't know how to do latex.
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    (Original post by Mystery.)
    The question is:
    General solution of
    d^2y/dx^2−4dydx+4y=2e^2x
    I have got the complementary function as (A+Bx)e2x=0 but when finding the Particular integral I substitute back I am getting zero? I have tried both y=Ce2xand Cxe2x ?

    I tried Cx^2e^2x because I realised it needs to be independent of the homogeneous equation but then I get two variables C and x to solve in the end?
    Spoiler:
    Show
    Sorry, don't know how to do latex.
    Can I see your working?
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    (Original post by Kvothe the Arcane)
    Can I see your working?
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    (Original post by Mystery.)
    Name:  IMG_1116.jpg
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Size:  386.8 KB
    Second derivitive of y is wrong.


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