\[ (a+x) y(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0708558 (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 = 0.146 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl M}_{-{\frac {i}{2}}a,\,{\frac {1}{2}}}\left (2\,ix\right )}+{\it \_C2}\,{{\sl W}_{-{\frac {i}{2}}a,\,{\frac {1}{2}}}\left (2\,ix\right )} \right \} \]