\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( ax-{b}^{2} \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.069509 (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 = 0.016 (sec), leaf count = 51 \[ \left \{ y \left ( x \right ) ={{\it \_C1}{{\sl J}_{\sqrt {4\,{b}^{2}+1} }\left (2\,\sqrt {a}\sqrt {x}\right )}{\frac {1}{\sqrt {x}}}}+{{\it \_C2 }{{\sl Y}_{\sqrt {4\,{b}^{2}+1}}\left (2\,\sqrt {a}\sqrt {x}\right )}{ \frac {1}{\sqrt {x}}}} \right \} \]