What is the solution for x((dy}{dx})-y=(\frac{x^3)/y)e^{y/x} ?

The solution for x((dy}{dx})-y=(\frac{x^3)/y)e^{y/x} is y=-\W((x+c_{1})/e)x-x

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x((dy}{dx})-y=(\frac{x^3)/y)e^{y/x}

x (\frac{d y}{d x}) - y = (\frac{x ^{3}}{y}) e^{\frac{y}{x}}

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

Solution steps

x (\frac{d y}{d x}) - y = (\frac{x ^{3}}{y}) e^{\frac{y}{x}}

Solve using substitution:

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

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

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What is the solution for x((dy}{dx})-y=(\frac{x^3)/y)e^{y/x} ?
The solution for x((dy}{dx})-y=(\frac{x^3)/y)e^{y/x} is y=-\W((x+c_{1})/e)x-x