# Differential Equation solve differential equation (dy)/( dx) =((3x-y-6))/((x+y+2)) I tried to do this but it´s first order and posible is separable variables

Differential Equation
solve differential equation
$\frac{dy}{dx}=\frac{\left(3x-y-6\right)}{\left(x+y+2\right)}$
I tried to do this but it´s first order and posible is separable variables
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silenthunter440
From $\frac{dy}{dx}=\frac{\left(3x-y-6\right)}{\left(x+y+2\right)}$, we have
$\left(x+y+2\right)dy-\left(3x-y-6\right)dx=0$
We look for $F\left(x,y\right)$ such that
${F}_{y}=x+y+2$
${F}_{y}=x+y+2$
${F}_{x}=-\left(3x-y-6\right)$
Solve for F, $F\left(x,y\right)=xy+\frac{{y}^{2}}{2}+2y-\frac{3{x}^{2}}{2}+6x$
The solution is F(x,y) = Constant.