What is the solution for x^2y^{''}=y^'+(y^')^2 ?

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

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x^2y^{''}=y^'+(y^')^2

x^{2} y^{^{''}} = y^{^{'}} + (y^{^{'}})^{2}

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

Solution steps

x^{2} y^{''} (x) = y^{'} (x) + (y^{'} (x))^{2}

Solve using substitution:

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

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

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