\[ (a+x) y(x)+x y''(x)+y'(x)=0 \] ✓ Mathematica : cpu = 0.0093284 (sec), leaf count = 61
DSolve[(a + x)*y[x] + Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{-i x} U\left (\frac {1}{2} i (a-i),1,2 i x\right )+c_2 e^{-i x} L_{-\frac {1}{2} i (a-i)}(2 i x)\right \}\right \}\] ✓ Maple : cpu = 0.063 (sec), leaf count = 39
dsolve(x*diff(diff(y(x),x),x)+diff(y(x),x)+(x+a)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-i x} \left (\KummerU \left (\frac {1}{2}+\frac {i a}{2}, 1, 2 i x \right ) c_{2}+\KummerM \left (\frac {1}{2}+\frac {i a}{2}, 1, 2 i x \right ) c_{1}\right )\]