Computing A and B such that A*(\partial f / \partial x) + B*(\partial f / \partial y) = 1.

> fxpartial:=diff(f(x,y),x);

> fypartial:=diff(f(x,y),y);

Here before using the GCD function on polynomials, we make the following adjustment.... namely we assume that B = y *C and then solve for A and C such that

A*fxpartial + C*2(x^3 + x*c1 + c2) = 1.

That we we are taking the gcd with respect to just one variable, namely x.

> lydia:=2*(x^3 + x*c1 + c2);

> gcdex(fxpartial,lydia,x, 's', 't');

> A:=simplify(s);

> B:=y*simplify(t);

> Ap:=A^p;

> Bp:=B^p;

>