Answer & Explanation
There is one obvious solution .
We have divided by , so this is ok only for points such that .
To get , we need
The idea is that in differential equations of the form , the Bernoulli equations, you can do the variable change , and your equation becomes
Multiplying through by , this is the same as
So the idea is that if you choose so that , in other words, , your equation becomes first-order linear and you can solve it using first-order linear methods. In this case, and you make the variable change