\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( ax+b \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +cy \left ( x \right ) =0} \]
Mathematica: cpu = 0.082511 (sec), leaf count = 266 \[ \left \{\left \{y(x)\to c_1 i^{-\sqrt {a^2-2 a-4 c+1}+a-1} b^{\frac {1}{2} \left (-\sqrt {a^2-2 a-4 c+1}+a-1\right )} \left (\frac {1}{x}\right )^{\frac {1}{2} \left (-\sqrt {a^2-2 a-4 c+1}+a-1\right )} \, _1F_1\left (\frac {a}{2}-\frac {1}{2} \sqrt {a^2-2 a-4 c+1}-\frac {1}{2};1-\sqrt {a^2-2 a-4 c+1};\frac {b}{x}\right )+c_2 i^{\sqrt {a^2-2 a-4 c+1}+a-1} b^{\frac {1}{2} \left (\sqrt {a^2-2 a-4 c+1}+a-1\right )} \left (\frac {1}{x}\right )^{\frac {1}{2} \left (\sqrt {a^2-2 a-4 c+1}+a-1\right )} \, _1F_1\left (\frac {a}{2}+\frac {1}{2} \sqrt {a^2-2 a-4 c+1}-\frac {1}{2};\sqrt {a^2-2 a-4 c+1}+1;\frac {b}{x}\right )\right \}\right \} \]
Maple: cpu = 0.125 (sec), leaf count = 135 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{-{\frac {1}{2}\sqrt {{a} ^{2}-2\,a-4\,c+1}}-{\frac {a}{2}}+{\frac {1}{2}}}{{\sl M}\left (-{ \frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}} ,\,1+\sqrt {{a}^{2}-2\,a-4\,c+1},\,{\frac {b}{x}}\right )}+{\it \_C2}\, {x}^{-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}-{\frac {a}{2}}+{\frac {1}{2}}}{{\sl U}\left (-{\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a -4\,c+1}}+{\frac {a}{2}},\,1+\sqrt {{a}^{2}-2\,a-4\,c+1},\,{\frac {b}{ x}}\right )} \right \} \]