\[ (a+x) y(x)+x y''(x)+y'(x)=0 \] ✓ Mathematica : cpu = 0.0139862 (sec), leaf count = 55
\[\left \{\left \{y(x)\to e^{-i x} \left (c_1 U\left (\frac {i a}{2}+\frac {1}{2},1,2 i x\right )+c_2 L_{-\frac {1}{2} i (a-i)}(2 i x)\right )\right \}\right \}\]
✓ Maple : cpu = 0.076 (sec), leaf count = 39
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-ix}} \left ( {{\sl U}\left ({\frac {1}{2}}+{\frac {i}{2}}a,\,1,\,2\,ix\right )}{\it \_C2}+{{\sl M}\left ({\frac {1}{2}}+{\frac {i}{2}}a,\,1,\,2\,ix\right )}{\it \_C1} \right ) \right \} \]