What is the solution for (dx)/(dy)=xy+x-2y-2 ?

The solution for (dx)/(dy)=xy+x-2y-2 is x=e^{y+(y^2)/2+c_{1}}+2

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(dx)/(dy)=xy+x-2y-2

\frac{d x}{d y} = x y + x - 2 y - 2

x = e^{y + \frac{y ^{2}}{2} + c_{1}} + 2

Solution steps

\frac{d x}{d y} = x y + x - 2 y - 2

Solve separable ODE:

x = e^{y + \frac{y ^{2}}{2} + c_{1}} + 2

x = e^{y + \frac{y ^{2}}{2} + c_{1}} + 2

\frac{d y}{d x} = \frac{( x y ^{2} - x )}{y}

y^{^{'}} = \frac{2 x}{e ^{2 y}}

x 1 + y^{2} d x - d y = 0

\frac{d y}{y} = \frac{d x}{( x - 9 ) ^{2} - 5 ^{2}}

y^{^{'}} = - \frac{0.1 y}{0.5 - 0.025 x}

What is the solution for (dx)/(dy)=xy+x-2y-2 ?
The solution for (dx)/(dy)=xy+x-2y-2 is x=e^{y+(y^2)/2+c_{1}}+2