One incorrect step was this:
which is incorrect.
You have to do a substitution thus:
How does that change things?
In connection with a thread posted earlier Anteeks was having problems with the equation: .
If you solve this with an integrating factor you get a factor of .
If you plug in the initial condition, , and this satisfies the original equation.
However, Mr Fantastic pointed out that the equation was seperable, and indeed it is. But when I solve it that way:
This does not satisfiy the original equation, so can't be right, but I don't see what I'm doing wrong.