\[ (a+x) y(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0678056 (sec), leaf count = 72
DSolve[(a + x)*y[x] + x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 e^{-i x} x \, _1F_1\left (1-\frac {1}{4} i (-2 (a-2)-4);2;2 i x\right )+c_1 e^{-i x} x U\left (1-\frac {1}{4} i (-2 (a-2)-4),2,2 i x\right )\right \}\right \}\] ✓ Maple : cpu = 0.044 (sec), leaf count = 29
dsolve(x*diff(diff(y(x),x),x)+(x+a)*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \WhittakerM \left (-\frac {i a}{2}, \frac {1}{2}, 2 i x \right )+c_{2} \WhittakerW \left (-\frac {i a}{2}, \frac {1}{2}, 2 i x \right )\]