\[ \boxed { 2\,x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( x-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ay \left ( x \right ) =0} \]
Mathematica: cpu = 0.010001 (sec), leaf count = 58 \[ \left \{\left \{y(x)\to c_1 \sqrt {x} U\left (\frac {1}{2} (1-2 a),\frac {3}{2},\frac {x}{2}\right )+c_2 \sqrt {x} L_{\frac {1}{2} (2 a-1)}^{\frac {1}{2}}\left (\frac {x}{2}\right )\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 35 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {x}{{\sl M}\left (-a+{ \frac {1}{2}},\,{\frac {3}{2}},\,{\frac {x}{2}}\right )}+{\it \_C2}\, \sqrt {x}{{\sl U}\left (-a+{\frac {1}{2}},\,{\frac {3}{2}},\,{\frac {x }{2}}\right )} \right \} \]