\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( ax+b \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.075510 (sec), leaf count = 212 \[ \left \{\left \{y(x)\to c_2 a^{\frac {1}{2} \left (\sqrt {1-4 b}+1\right )-\frac {1}{2} \sqrt {1-4 b}} x^{\frac {1}{2} \left (\sqrt {1-4 b}+1\right )-\frac {1}{2} \sqrt {1-4 b}} \Gamma \left (\sqrt {1-4 b}+1\right ) J_{\sqrt {1-4 b}}\left (2 \sqrt {a} \sqrt {x}\right )+c_1 a^{\frac {1}{2} \left (1-\sqrt {1-4 b}\right )+\frac {1}{2} \sqrt {1-4 b}} x^{\frac {1}{2} \left (1-\sqrt {1-4 b}\right )+\frac {1}{2} \sqrt {1-4 b}} \Gamma \left (1-\sqrt {1-4 b}\right ) J_{-\sqrt {1-4 b}}\left (2 \sqrt {a} \sqrt {x}\right )\right \}\right \} \]
Maple: cpu = 0.015 (sec), leaf count = 47 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {x}{{\sl J}_{\sqrt {1-4 \,b}}\left (2\,\sqrt {a}\sqrt {x}\right )}+{\it \_C2}\,\sqrt {x}{{\sl Y} _{\sqrt {1-4\,b}}\left (2\,\sqrt {a}\sqrt {x}\right )} \right \} \]