\[ (a+x) y(x)+x y''(x)+y'(x)=0 \] ✓ Mathematica : cpu = 0.0157813 (sec), leaf count = 61
\[\left \{\left \{y(x)\to c_1 e^{-i x} U\left (\frac {1}{2} i (a-i),1,2 i x\right )+c_2 e^{-i x} L_{-\frac {1}{2} i (a-i)}(2 i x)\right \}\right \}\]
✓ Maple : cpu = 0.067 (sec), leaf count = 43
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-ix}}{{\sl M}\left ({\frac {1}{2}}+{\frac {i}{2}}a,\,1,\,2\,ix\right )}+{\it \_C2}\,{{\rm e}^{-ix}}{{\sl U}\left ({\frac {1}{2}}+{\frac {i}{2}}a,\,1,\,2\,ix\right )} \right \} \]