Frobenius & Special Functions · Medium problem

Let $y_1, y_2$ be two solutions of Legendre's equation $(1 - x^2)y'' - 2xy' + 2y = 0$ on $-1 < x < 1$ with Wronskian $W(0) = 1$. Compute $W\!\left(\tfrac12\right)$. Express your answer as a common fraction.