What is the solution for y^'y^{-2}+xy^{-1}=x ?

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

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y^'y^{-2}+xy^{-1}=x

y^{^{'}} y^{- 2} + x y^{- 1} = x

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

Solution steps

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

Solve separable ODE:

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

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

\frac{5 x + 2}{12 x + 5}

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