The function depends on and but the equation only involves , hence it can be seen as an ordinary differential equation.

Let be fixed. Write . Then is a function of 1 variable and for every . Let , so that . This is a linear first order differential equation: we know how to solve it. Since , there exists such that . Hence, by integration, for some .

However, the "constants" and depend on which was fixed before, hence we should write and : . This is it.