nonhomogenous.." (D^2 -1) = e^x + 1 "...

I need someone to solve it in variation of parameters method.. the answer in my book is y=C1e^x + C2e^-x + (xe^x/2) - (e^x/4) -1 ... tried doing it but my answer has an extra (-e^-x/4). checked my solution several times already but my answer is still the same. need someone to confirm this.

EDIT: I exchange e^x/2 to e^2/4 .. typoz -_-

Question

nonhomogenous.." (D^2 -1) = e^x + 1  "...

I need someone to solve it in variation of parameters method.. the answer in my book is y=C1e^x + C2e^-x + (xe^x/2) - (e^x/4) -1  ... tried doing it but my answer has an extra (-e^-x/4). checked my solution several times already but my answer is still the same. need someone to confirm this.

EDIT: I exchange e^x/2 to e^2/4 .. typoz -_-

turingtest · Answer

$$y_1=e^x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y_2=e^{-x}$$$$y_p=-y_1\int\frac{f(x)y_2}{W}dx+y_2\int\frac{f(x)y_1}Wdx$$What did you get for the Wronskian?

phi · Answer

can't you combine
C2e^-x +(-e^-x/4)    
C3 e^-x  (just a different constant)

anonymous · Answer

oh.. tried solving it  again using TuringTest's equation.. i got 

|dw:1349890567934:dw|    ..still got the same answer from my solution earlier.. maybe my book is wrong.. i should get a new one.