\[ \boxed { x \left ( x-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( ax+b \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +cy \left ( x \right ) =0} \]
Mathematica: cpu = 0.162021 (sec), leaf count = 146 \[ \left \{\left \{y(x)\to (-1)^{b+1} c_2 x^{b+1} \, _2F_1\left (\frac {a}{2}+b-\frac {1}{2} \sqrt {a^2-2 a-4 c+1}+\frac {1}{2},\frac {a}{2}+b+\frac {1}{2} \sqrt {a^2-2 a-4 c+1}+\frac {1}{2};b+2;x\right )+c_1 \, _2F_1\left (\frac {a}{2}-\frac {1}{2} \sqrt {a^2-2 a-4 c+1}-\frac {1}{2},\frac {a}{2}+\frac {1}{2} \sqrt {a^2-2 a-4 c+1}-\frac {1}{2};-b;x\right )\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 110 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, {\mbox {$_2$F$_1$}(-{\frac {1}{2}}-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}},-{\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}};\,-b;\,x)} +{\it \_C2}\,{x}^{b+1} {\mbox {$_2$F$_1$}({\frac {1}{2}}-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}}+b,{\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}}+b;\,b+2;\,x)} \right \} \]