The differential equationdydx$=6+15$x$+14$y$+35$xyhas 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 formF$($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$)=$