\[ \boxed { x \left ( {x}^{2}-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( a{x}^{2}+b \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +cxy \left ( x \right ) =0} \]
Mathematica: cpu = 0.293537 (sec), leaf count = 172 \[ \left \{\left \{y(x)\to c_1 \, _2F_1\left (\frac {a}{4}-\frac {1}{4} \sqrt {a^2-2 a-4 c+1}-\frac {1}{4},\frac {a}{4}+\frac {1}{4} \sqrt {a^2-2 a-4 c+1}-\frac {1}{4};\frac {1}{2}-\frac {b}{2};x^2\right )+i^{b+1} c_2 x^{b+1} \, _2F_1\left (\frac {a}{4}+\frac {b}{2}-\frac {1}{4} \sqrt {a^2-2 a-4 c+1}+\frac {1}{4},\frac {a}{4}+\frac {b}{2}+\frac {1}{4} \sqrt {a^2-2 a-4 c+1}+\frac {1}{4};\frac {b}{2}+\frac {3}{2};x^2\right )\right \}\right \} \]
Maple: cpu = 0.094 (sec), leaf count = 122 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, {\mbox {$_2$F$_1$}(-{\frac {1}{4}}+{\frac {a}{4}}-{\frac {1}{4}\sqrt {{a}^{2}-2\,a-4\,c+1}},-{\frac {1}{4}}+{\frac {a}{4}}+{\frac {1}{4}\sqrt {{a}^{2}-2\,a-4\,c+1}};\,{\frac {1}{2}}-{\frac {b}{2}};\,{x}^{2})} +{\it \_C2}\,{x}^{b+1} {\mbox {$_2$F$_1$}({\frac {1}{4}}+{\frac {a}{4}}+{\frac {b}{2}}+{\frac {1}{4}\sqrt {{a}^{2}-2\,a-4\,c+1}},{\frac {1}{4}}+{\frac {a}{4}}+{\frac {b}{2}}-{\frac {1}{4}\sqrt {{a}^{2}-2\,a-4\,c+1}};\,{\frac {3}{2}}+{\frac {b}{2}};\,{x}^{2})} \right \} \]