Answer
$$y = -x\ln(\ln(x)+C)$$
Work Step by Step
\begin{align*}
y &= xv \\
y' &= xv' + v \\
x(xv' + v) &= xv + xe^{\frac{y}{x}} \\
x^2v' + xv &= xv + xe^{v} \\
x^2v' &= xe^{v} \\
v' &= \frac{e^{v}}{x} \\
\int \frac{dv}{e^{v}} &= \int \frac{dx}{x} \\
-e^{-v} &= \ln(x) + C \\
v &= -\ln(\ln(x) + C) \\
y &= -x\ln(\ln(x) + C)
\end{align*}
