I wonder if you're switching problems mid-way here? I get the following:
Just a comment @dw - your method would work fine if you were given IC's
but you're not. You're given
Some of it works but you're still left with two equations to solve. Adrian's method is much more natural and direct.
Next, dw, with your two equations for C and D, eliminate C and D and get a single equation for or .
Is this much correct?
The solution is:
I have been unable to manipulate my solution in order to obtain the books. I am guessing I am wrong, or I am unable to make a slick substitution with an identity.