Is the back of the book wrong? Solving a Differential Equation with Cosh(x)

[Sparky_]

Homework Statement

Solve : y'' -y = cosh(x)

Homework Equations

The Attempt at a Solution

the attempt is attached.

The answer in the back of the book agree with part of mine. However, the circled part - the part with 1/8 as a coefficient on e^x terms. It's circled on the bottom.

Either the back of the book is wrong (and I'm correct) or this term should cancel and I've missed something.
Help?

Thanks
-Sparky_

 

[Dick]

The circled term is a solution to the homogeneous equation y''-y=0. It can be absorbed into the c1*exp(x)+c2*exp(-x).