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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} = - \frac{7 sin ( 3 x )}{2 y}

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

(x^{2} + 9) \frac{d y}{d x} + x y = 0

\frac{d y}{d x} = \frac{6 ( 1 + x )}{x y}

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

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