What is the solution for (dy)/(dx)x^2*(1+y)=y^2(x-1) ?

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

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(dy)/(dx)x^2*(1+y)=y^2(x-1)

\frac{d y}{d x} x^{2} \cdot (1 + y) = y^{2} (x - 1)

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

Solution steps

\frac{d y}{d x} x^{2} \cdot (1 + y) = y^{2} (x - 1)

Solve separable ODE:

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

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

x + x y + y^{^{'}} = 0

\frac{d y}{d x} = 2 e^{x - y}, y (0) = ln (4)

\frac{d y}{d x} = \frac{4 y}{1 + x}

y^{^{'}} = \frac{( 2 y + 3 )}{x ^{2}}

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

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