# Math Help - Variation of Parameters

1. ## 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

2. 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)

3. 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

4. I edited my last post to make that exact point as at first I did the same thing