I'll have a go of it now...
Edit: I'm going to assume that you've made a typo, because if it involves it is near impossible to get it to the required form
So I'll fix the typo so that it should say instead. Then it is easy to get to the required form
So, the original DE should be (I think...)
Some rearranging will give you
Here so .
So make the substitution
Now find . Notice that .
So, when substituting everything into the DE, it becomes
This is first order linear, so can be solved using an integrating factor.