Example: Solve .

Here

> N:=(x,y)->3*x^2-y^2;M:=(x,y)->-2*x*y;

> diff(M(x,y),y)-diff(N(x,y),x);

Since the difference is not zero, this is not an exact equation. But

> %/M(x,y);

is an equation of only so we can solve it using an ir=#000000> only so we can solve it using an integrating factor.

> K:=unapply(-%,(x,y));exp(int(K(x,y),y));

So if we multiply the wole equation with , the resulting equation will be exact.

> M:=(x,y)->1/y^4*(-2*x*y);N:=(x,y)->1/y^4*(3*x^2-y^2);

> Ex;

Hence the solution is .