Frobenius & Special Functions · Hard problem

To study $x(1 - x)y'' + (1 - 4x)y' - 2y = 0$ for large $x$, substitute $x = \dfrac1t$ and $y(x) = w(t)$. The point $t = 0$ is a regular singular point of the resulting equation for $w$. Compute the product of its two indicial roots.