Well, I don't know about inspection, but the substitution renders the equation separable:
and hence the DE becomes
Here is what do you want:
Your equation is ready for integrating now.
Again, equation (1) is equivalent to the last equation in Ackbeet's reply.
Another way ,if you are intersted , :
We have ... (2)
Multiplying (2) by and substituting will give you a linear equation.