\[ a y(x)+x y''(x)-y'(x)=0 \] ✓ Mathematica : cpu = 0.0197088 (sec), leaf count = 46
DSolve[a*y[x] - Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to 2 a c_1 x J_2\left (2 \sqrt {a} \sqrt {x}\right )-2 a c_2 x Y_2\left (2 \sqrt {a} \sqrt {x}\right )\right \}\right \}\] ✓ Maple : cpu = 0.01 (sec), leaf count = 31
dsolve(x*diff(diff(y(x),x),x)-diff(y(x),x)+a*y(x)=0,y(x))
\[y \left (x \right ) = x \left (\BesselY \left (2, 2 \sqrt {a}\, \sqrt {x}\right ) c_{2}+\BesselJ \left (2, 2 \sqrt {a}\, \sqrt {x}\right ) c_{1}\right )\]