What is the solution for (dy)/(dx)=(xy-y)/(y+1) ?

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

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(dy)/(dx)=(xy-y)/(y+1)

\frac{d y}{d x} = \frac{x y - y}{y + 1}

y = W (\frac{1}{e ^{\frac{- x ^{2} + 2 x - c _{1}}{2}}})

Solution steps

\frac{d y}{d x} = \frac{x y - y}{y + 1}

Solve separable ODE:

y = W (\frac{1}{e ^{\frac{- x ^{2} + 2 x - c _{1}}{2}}})

y = W (\frac{1}{e ^{\frac{- x ^{2} + 2 x - c _{1}}{2}}})

x \to \infty lim (\frac{x}{3 ^{2 x + 1}})

\frac{d}{d x} (\frac{x}{arctan ( x )})

\frac{d y}{d x}, y sin (\frac{1}{y}) = 1 - x y

\frac{\partial}{\partial y} (x y e^{x})

\int x - x^{3} d x

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