Let a curve y=f(x) pass through the points (0,5) and ( log_e 2, k). If the curve satisfies the differential equation 2(3+y) e^2 x d x-(7+e^2 x) d…

Let a curve $\displaystyle y=f(x)$ pass through the points $\displaystyle (0,5)$ and $\displaystyle \left(\log _e 2, k\right)$. If the curve satisfies the differential equation $\displaystyle 2(3+y) e^{2 x} d x-\left(7+e^{2 x}\right) d y=0$, then $\displaystyle k$ is equal to