The differential equation

$\frac{dy}{dx}=\frac{10x8}{9y^{2}10y4}$

has an implicit general solution of the form $F(x,y)=K,$ where $K$ is an arbitary constant.

In fact, because the differential equation is separable, we can define the solution curve implicitly by a function in the form

$F(x,y)=G(x)H(y)=K$

Find such a solution and then give the related functions requested.

$F(x,y)=G(x)H(y)=$