\[ y(x) \left (a x-b^2\right )+x^2 y''(x)+2 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0701869 (sec), leaf count = 236
\[\left \{\left \{y(x)\to c_1 a^{\frac {1}{2} \left (-\sqrt {4 b^2+1}-1\right )+\frac {1}{2} \sqrt {4 b^2+1}} x^{\frac {1}{2} \left (-\sqrt {4 b^2+1}-1\right )+\frac {1}{2} \sqrt {4 b^2+1}} \Gamma \left (1-\sqrt {4 b^2+1}\right ) J_{-\sqrt {4 b^2+1}}\left (2 \sqrt {a} \sqrt {x}\right )+c_2 a^{\frac {1}{2} \left (\sqrt {4 b^2+1}-1\right )-\frac {1}{2} \sqrt {4 b^2+1}} x^{\frac {1}{2} \left (\sqrt {4 b^2+1}-1\right )-\frac {1}{2} \sqrt {4 b^2+1}} \Gamma \left (\sqrt {4 b^2+1}+1\right ) J_{\sqrt {4 b^2+1}}\left (2 \sqrt {a} \sqrt {x}\right )\right \}\right \}\]
✓ Maple : cpu = 0.025 (sec), leaf count = 51
\[ \left \{ y \left ( x \right ) ={{\it \_C1}{{\sl J}_{\sqrt {4\,{b}^{2}+1}}\left (2\,\sqrt {a}\sqrt {x}\right )}{\frac {1}{\sqrt {x}}}}+{{\it \_C2}{{\sl Y}_{\sqrt {4\,{b}^{2}+1}}\left (2\,\sqrt {a}\sqrt {x}\right )}{\frac {1}{\sqrt {x}}}} \right \} \]