Chapter 2, miscellaneous exercises no. 4:

I made it homogeneous:

Then I substituted which makes it separable:

and so

Now the nightmare begins. The integral on the LHS seems to be tractable only if I try the substitution

This leads to:

Converting the hyp funcs to exps:

which gets us to

To get back to and thence , I substitute back using the formula for from which I end up with the answer to my diffeq:

So far so good, but the answer as given in the book is:

Can these two results be reconciled? I fear not. Can anyone work it through and see whether (a) I've made a mistake somewhere, or (b) I haven't followed through far enough?