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

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

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(dy)/(dx)= y/x+e^{-y/x}

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

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

Solution steps

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

Solve using substitution:

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

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

y = 5 x^{2} - x^{3}

x \to 2 lim (\frac{x ^{2} + 4}{x - 2})

\frac{\partial}{\partial x} (3 x^{2} \cdot e^{x^{2} y})

cos ((2 x^{2} + 1)^{7})

\frac{d}{d x} (\frac{2 x ^{5} + 5}{x ^{3}})

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