Differential Equations

Let $y : (-\infty, \infty) \to (0, \infty)$ be the solution of the differential equation

\(\frac{dy}{dx} = \frac{e^{5x} y^3 + y^3}{e^x + e^x y^4},\)

satisfying $y(0) = \frac{1}{\sqrt{2}}$. Then the value of $y(\log_e 2)$ is