What is the solution for x^2y^'-y-y^2=0 ?

The solution for x^2y^'-y-y^2=0 is y=(e^{c_{1}})/(e^{1/x)-e^{c_{1}}}

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x^2y^'-y-y^2=0

x^{2} y^{^{'}} - y - y^{2} = 0

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

Solution steps

x^{2} y^{'} (x) - y - y^{2} = 0

Solve separable ODE:

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

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

\frac{d y}{d x} y = x e^{- 6 x} + 6 e^{- x} + x^{7}

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

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

y = e^{\frac{3}{2 x}} \frac{d y}{d x}

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

What is the solution for x^2y^'-y-y^2=0 ?
The solution for x^2y^'-y-y^2=0 is y=(e^{c_{1}})/(e^{1/x)-e^{c_{1}}}