Let y=y(x) be the solution of the differential equation (1-x^2) d y=[x y+(x^3+2) √(3(1-x^2))] d x, -1<x<1, y(0)=0. If y(1/2)=m/n, m and n are…

Let $\displaystyle y=y(x)$ be the solution of the differential equation $\displaystyle \left(1-x^2\right) \mathrm{d} y=\left[x y+\left(x^3+2\right) \sqrt{3\left(1-x^2\right)}\right] \mathrm{d} x$, $\displaystyle -1<x<1, y(0)=0$. If $\displaystyle y\left(\frac{1}{2}\right)=\frac{m}{n}$, m and n are co-prime numbers, then $\displaystyle m+n$ is equal to $\displaystyle \_\_\_\_$.