Using variation of parameters, solve for the general solution of:
$\displaystyle (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
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)
In my answer I keep getting an extra term "$\displaystyle -xe^x $" and according in the book the answer is y = yc + $\displaystyle e^xln(1 + e^x) $...where yc is the complimentary solution. So it is possible for $\displaystyle -xe^x $ to be absorbed by one of the terms in the complementary solution...Now I know thank you