\[ \boxed { 2\,x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( 2\,x-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ay \left ( x \right ) =0} \]
Mathematica: cpu = 0.010501 (sec), leaf count = 48 \[ \left \{\left \{y(x)\to c_1 \sqrt {x} U\left (\frac {1-a}{2},\frac {3}{2},x\right )+c_2 \sqrt {x} L_{\frac {a-1}{2}}^{\frac {1}{2}}(x)\right \}\right \} \]
Maple: cpu = 0.063 (sec), leaf count = 31 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {x}{{\sl M}\left (-{ \frac {a}{2}}+{\frac {1}{2}},\,{\frac {3}{2}},\,x\right )}+{\it \_C2}\, \sqrt {x}{{\sl U}\left (-{\frac {a}{2}}+{\frac {1}{2}},\,{\frac {3}{2}} ,\,x\right )} \right \} \]