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The differential equation

`(dy)/(dx)=9+27x+15y+45xy`

has an implicit general solution of the form

`F(x,y)=K`

. 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)=`