Given the differential equation
where $\,M\,$ and $\,N\,$ may be functions of both $\,x\,$ and $\,y\,$. If the above equation can be transformed into the form
where $\,f(x)\,$ is a function of $\,x\,$ alone and $\,f(y)\,$ is a function of $\,y\,$ alone, equation (1) is called variables separable.
To find the general solution of equation (1), simply equate the integral of equation (2) to a constant $\,c\,$. Thus, the general solution is