Frobenius & Special Functions · Challenge problem

The equation $xy'' + (1-x)y' + 2y = 0$ has a double indicial root $r=0$ at $x=0$ and a polynomial Frobenius solution $y = a_0 + a_1x + a_2x^2$ normalised by $a_0=1$. This polynomial has two real roots. Find the larger one. Give an exact answer.