Frobenius & Special Functions · Hard problem

Solve the third-order Cauchy–Euler problem $x^3y^{\prime\prime\prime} - 3x^2y'' + 6xy' - 6y = 0$, $y(1) = 0$, $y'(1) = 0$, $y''(1) = 2$, and compute $y(3)$.