Let us define another change of variable for our dependent variable: choose .

Then , , and thus our equation becomes

This is a nonhomogenous first order linear differential equation. We can see by substitution that is a solution. Thus, we find and add to that the general solution for the corresponding homogenous equation

, which is separable:

Thus the solution to is , and from there you can convert back into w, and then into .

--Kevin C.