What is the solution for (xdy)/(dx)=y+xe^{-y/x} ?

The solution for (xdy)/(dx)=y+xe^{-y/x} is y=ln(ln(x)+c_{1})x

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(xdy)/(dx)=y+xe^{-y/x}

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

y = ln (ln (x) + c_{1}) x

Solution steps

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

Solve using substitution:

y = ln (ln (x) + c_{1}) x

y = ln (ln (x) + c_{1}) x

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What is the solution for (xdy)/(dx)=y+xe^{-y/x} ?
The solution for (xdy)/(dx)=y+xe^{-y/x} is y=ln(ln(x)+c_{1})x