\[ y(x) \left (a x-b^2\right )+x^2 y''(x)+2 x y'(x)=0 \] ✓ Mathematica : cpu = 0.050154 (sec), leaf count = 236
DSolve[(-b^2 + a*x)*y[x] + 2*x*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 a^{\frac {1}{2} \left (-\sqrt {4 b^2+1}-1\right )+\frac {1}{2} \sqrt {4 b^2+1}} x^{\frac {1}{2} \left (-\sqrt {4 b^2+1}-1\right )+\frac {1}{2} \sqrt {4 b^2+1}} \Gamma \left (1-\sqrt {4 b^2+1}\right ) J_{-\sqrt {4 b^2+1}}\left (2 \sqrt {a} \sqrt {x}\right )+c_2 a^{\frac {1}{2} \left (\sqrt {4 b^2+1}-1\right )-\frac {1}{2} \sqrt {4 b^2+1}} x^{\frac {1}{2} \left (\sqrt {4 b^2+1}-1\right )-\frac {1}{2} \sqrt {4 b^2+1}} \Gamma \left (\sqrt {4 b^2+1}+1\right ) J_{\sqrt {4 b^2+1}}\left (2 \sqrt {a} \sqrt {x}\right )\right \}\right \}\] ✓ Maple : cpu = 0.032 (sec), leaf count = 49
dsolve(x^2*diff(diff(y(x),x),x)+2*x*diff(y(x),x)+(a*x-b^2)*y(x)=0,y(x))
\[y \left (x \right ) = \frac {c_{2} \BesselY \left (\sqrt {4 b^{2}+1}, 2 \sqrt {a}\, \sqrt {x}\right )+c_{1} \BesselJ \left (\sqrt {4 b^{2}+1}, 2 \sqrt {a}\, \sqrt {x}\right )}{\sqrt {x}}\]