As you saw, sometimes to separate variables involves some tricky algebraic factorization. So before going into trial and error waters of algebra, you better use Theorem to check if it can be done. Thus if we don't see right away how to separate variables let's check if it can be done at all. For the previous example we would have to check if . Of co urse we do this in Maple. But before we proceed Maple remembers that is a function of . To ''erase'' Maple's memory we use Maple command restart.

> restart;

First we define as a function of two variables.

> f:=(x,y)->2*x^2+y-x^2*y+x*y-2*x-2;

To get we apply Maple command diff as follows

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

Now we will check if .

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

> simplify(%);