What is the solution for xyy^'=x^2e^{y/x}+y^2 ?

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

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xyy^'=x^2e^{y/x}+y^2

x y y^{^{'}} = x^{2} e^{\frac{y}{x}} + y^{2}

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

Solution steps

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

Solve using substitution:

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

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

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