The differential equation dy/dx = 25+20x+40y+32xy
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 of F(x,y)=G(x)+H(y)=K
Find such a solution and then give the related functions requested for
F(x,y)=G(x)+H(y)=
The given equation can be rewritten as, .
The equation can be separated as,
Integrating, we get
Therefore,
.
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