\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\, \left ( x-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ay \left ( x \right ) =0} \]
Mathematica: cpu = 0.055007 (sec), leaf count = 158 \[ \left \{\left \{y(x)\to 2^{\frac {1}{2} \left (1-\sqrt {1-4 a}\right )} c_1 \left (\frac {1}{x}\right )^{\frac {1}{2} \left (1-\sqrt {1-4 a}\right )} \, _1F_1\left (\frac {1}{2}-\frac {1}{2} \sqrt {1-4 a};1-\sqrt {1-4 a};-\frac {2}{x}\right )+2^{\frac {1}{2} \left (\sqrt {1-4 a}+1\right )} c_2 \left (\frac {1}{x}\right )^{\frac {1}{2} \left (\sqrt {1-4 a}+1\right )} \, _1F_1\left (\frac {1}{2} \sqrt {1-4 a}+\frac {1}{2};\sqrt {1-4 a}+1;-\frac {2}{x}\right )\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 57 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{x}^{-1}}}\sqrt {{ x}^{-1}}{{\sl I}_{{\frac {1}{2}\sqrt {1-4\,a}}}\left ({x}^{-1}\right )}+ {\it \_C2}\,{{\rm e}^{-{x}^{-1}}}\sqrt {{x}^{-1}}{{\sl K}_{{\frac {1}{ 2}\sqrt {1-4\,a}}}\left ({x}^{-1}\right )} \right \} \]