Example where fails:

Checking first if a first order differential equation is separable would save us a lots of time as well it would save us from frustration. We ilustrate this on the following example.

Example: Solve . This equation is much simpler than previous one, yet as following shows it cannot be solved using separation of variables method.

> f:=(x,y)->1+x*y;

> f(x,y)*diff(f(x,y),x,y)-diff(f(x,y),x)*diff(f(x,y),y);

Since is not zero, this differential equation cannot be solved using separation of varibles method.