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# Second order linear differential equation, stuck on particular integral

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1. 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.
2. (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.
3. (Original post by Kvothe the Arcane)
4. (Original post by Mystery.)
Second derivitive of y is wrong.

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