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The differential equation

$\frac{dy}{dx}=10+4x+25y+10xy$

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

$F(x,y)=G(x)+H(y)=2x^2+10x+\frac{25y^2}{2}$

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