\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( x+a \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.096012 (sec), leaf count = 72 \[ \left \{\left \{y(x)\to c_2 e^{-i x} x \, _1F_1\left (1-\frac {1}{4} i (-2 (a-2)-4);2;2 i x\right )+c_1 e^{-i x} x U\left (1-\frac {1}{4} i (-2 (a-2)-4),2,2 i x\right )\right \}\right \} \]
Maple: cpu = 0.109 (sec), leaf count = 29 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl M}_{-{\frac {i}{2}}a,\, {\frac {1}{2}}}\left (2\,ix\right )}+{\it \_C2}\,{{\sl W}_{-{\frac {i}{2 }}a,\,{\frac {1}{2}}}\left (2\,ix\right )} \right \} \]