\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( {x}^{2}-2\,x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( x+a \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.018002 (sec), leaf count = 78 \[ \left \{\left \{y(x)\to c_1 e^{\frac {1}{2} (x-\log (x))} J_{\frac {1}{2} \sqrt {4 a+1}}\left (-\frac {i x}{2}\right )+c_2 e^{\frac {1}{2} (x-\log (x))} Y_{\frac {1}{2} \sqrt {4 a+1}}\left (-\frac {i x}{2}\right )\right \}\right \} \]
Maple: cpu = 0.032 (sec), leaf count = 49 \[ \left \{ y \left ( x \right ) ={{\it \_C1}{{\rm e}^{{\frac {x}{2}}}}{ {\sl I}_{{\frac {1}{2}\sqrt {4\,a+1}}}\left ({\frac {x}{2}}\right )}{ \frac {1}{\sqrt {x}}}}+{{\it \_C2}{{\rm e}^{{\frac {x}{2}}}}{{\sl K}_{ {\frac {1}{2}\sqrt {4\,a+1}}}\left ({\frac {x}{2}}\right )}{\frac {1}{ \sqrt {x}}}} \right \} \]