Differential Equations: JEE Main 2023 Mathematics question

If the solution curve of the differential equation $\left(y-2 \log _{e} x\right) d x+\left(x \log _{e} x^{2}\right) d y=0, x > 1$ passes through the points $\left(e, \frac{4}{3}\right)$ and $\left(e^{4}, \alpha\right)$, then $\alpha$ is equal to ____________.