\[ y(x) (a x+b)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0455905 (sec), leaf count = 212
DSolve[(b + a*x)*y[x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 a^{\frac {1}{2} \left (\sqrt {1-4 b}+1\right )-\frac {1}{2} \sqrt {1-4 b}} x^{\frac {1}{2} \left (\sqrt {1-4 b}+1\right )-\frac {1}{2} \sqrt {1-4 b}} \Gamma \left (\sqrt {1-4 b}+1\right ) J_{\sqrt {1-4 b}}\left (2 \sqrt {a} \sqrt {x}\right )+c_1 a^{\frac {1}{2} \left (1-\sqrt {1-4 b}\right )+\frac {1}{2} \sqrt {1-4 b}} x^{\frac {1}{2} \left (1-\sqrt {1-4 b}\right )+\frac {1}{2} \sqrt {1-4 b}} \Gamma \left (1-\sqrt {1-4 b}\right ) J_{-\sqrt {1-4 b}}\left (2 \sqrt {a} \sqrt {x}\right )\right \}\right \}\] ✓ Maple : cpu = 0.02 (sec), leaf count = 45
dsolve(x^2*diff(diff(y(x),x),x)+(a*x+b)*y(x)=0,y(x))
\[y \left (x \right ) = \sqrt {x}\, \left (\BesselY \left (\sqrt {1-4 b}, 2 \sqrt {a}\, \sqrt {x}\right ) c_{2}+\BesselJ \left (\sqrt {1-4 b}, 2 \sqrt {a}\, \sqrt {x}\right ) c_{1}\right )\]