If y=y(x) is the solution of the differential equation (1+e^2 x) (d y)/(d x)+2(1+y^2) e^x=0 and y(0)=0, then 6(y^′(0)+(y( log_e √ 3 ))^2) is equal to

If $\displaystyle y=y(x)$ is the solution of the differential equation $\displaystyle \left(1+e^{2 x}\right) \frac{d y}{d x}+2\left(1+y^2\right) e^x=0$ and $\displaystyle y(0)=0$, then $\displaystyle 6\left(y^{\prime}(0)+\left(y\left(\log _e \sqrt{3}\right)\right)^2\right)$ is equal to