\[ a y'(x)+b x y(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0145185 (sec), leaf count = 64
DSolve[b*x*y[x] + a*Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 x^{\frac {1-a}{2}} J_{\frac {a-1}{2}}\left (\sqrt {b} x\right )+c_2 x^{\frac {1-a}{2}} Y_{\frac {a-1}{2}}\left (\sqrt {b} x\right )\right \}\right \}\] ✓ Maple : cpu = 0.046 (sec), leaf count = 39
dsolve(x*diff(diff(y(x),x),x)+a*diff(y(x),x)+b*x*y(x)=0,y(x))
\[y \left (x \right ) = x^{-\frac {a}{2}+\frac {1}{2}} \left (\BesselY \left (\frac {a}{2}-\frac {1}{2}, \sqrt {b}\, x \right ) c_{2}+\BesselJ \left (\frac {a}{2}-\frac {1}{2}, \sqrt {b}\, x \right ) c_{1}\right )\]