\[ y''(x) \left (a x^2+b x+c\right )+(d x+f) y'(x)+g y(x)=0 \] ✓ Mathematica : cpu = 5.19027 (sec), leaf count = 498
\[\left \{\left \{y(x)\to c_1 \, _2F_1\left (-\frac {a-d+\sqrt {(a-d)^2-4 a g}}{2 a},\frac {-a+d+\sqrt {(a-d)^2-4 a g}}{2 a};\frac {\left (b+\sqrt {b^2-4 a c}\right ) d-2 a f}{2 a \sqrt {b^2-4 a c}};\frac {b+2 a x+\sqrt {b^2-4 a c}}{2 \sqrt {b^2-4 a c}}\right )-c_2 2^{\frac {\frac {b d}{\sqrt {b^2-4 a c}}+d}{2 a}-\frac {f}{\sqrt {b^2-4 a c}}-1} \exp \left (-\frac {i \pi \left (d \left (\sqrt {b^2-4 a c}+b\right )-2 a f\right )}{2 a \sqrt {b^2-4 a c}}\right ) \left (\frac {\sqrt {b^2-4 a c}+2 a x+b}{\sqrt {b^2-4 a c}}\right )^{-\frac {\frac {b d}{\sqrt {b^2-4 a c}}+d}{2 a}+\frac {f}{\sqrt {b^2-4 a c}}+1} \, _2F_1\left (\frac {\frac {2 f a}{\sqrt {b^2-4 a c}}+a-\frac {b d}{\sqrt {b^2-4 a c}}-\sqrt {(a-d)^2-4 a g}}{2 a},\frac {\frac {2 f a}{\sqrt {b^2-4 a c}}+a-\frac {b d}{\sqrt {b^2-4 a c}}+\sqrt {(a-d)^2-4 a g}}{2 a};-\frac {\frac {b d}{\sqrt {b^2-4 a c}}+d+a \left (-\frac {2 f}{\sqrt {b^2-4 a c}}-4\right )}{2 a};\frac {b+2 a x+\sqrt {b^2-4 a c}}{2 \sqrt {b^2-4 a c}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.784 (sec), leaf count = 501
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_2$F$_1$}({\frac {1}{2\,a} \left ( -a+d+\sqrt {{a}^{2}+ \left ( -2\,d-4\,g \right ) a+{d}^{2}} \right ) },-{\frac {1}{2\,a} \left ( a-d+\sqrt {{a}^{2}+ \left ( -2\,d-4\,g \right ) a+{d}^{2}} \right ) };\,{\frac {1}{2\,{a}^{2}} \left ( d\sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}a-2\,af+bd \right ) {\frac {1}{\sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}}}};\,{\frac {1}{8\,ac-2\,{b}^{2}} \left ( \left ( -2\,{a}^{2}x-ab \right ) \sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}+4\,ac-{b}^{2} \right ) })}+{\it \_C2}\, \left ( 2\,\sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}x{a}^{2}+\sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}ba-4\,ac+{b}^{2} \right ) ^{{\frac {1}{{a}^{2}} \left ( a \left ( a-{\frac {d}{2}} \right ) \sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}+af-{\frac {bd}{2}} \right ) {\frac {1}{\sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}}}}}{\mbox {$_2$F$_1$}({\frac {1}{2\,{a}^{2}} \left ( a \left ( a-\sqrt {{a}^{2}+ \left ( -2\,d-4\,g \right ) a+{d}^{2}} \right ) \sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}+2\,af-bd \right ) {\frac {1}{\sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}}}},{\frac {1}{2\,{a}^{2}} \left ( a \left ( a+\sqrt {{a}^{2}+ \left ( -2\,d-4\,g \right ) a+{d}^{2}} \right ) \sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}+2\,af-bd \right ) {\frac {1}{\sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}}}};\,{\frac {1}{2\,{a}^{2}} \left ( 4\,{a}^{2}\sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}-d\sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}a+2\,af-bd \right ) {\frac {1}{\sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}}}};\,{\frac {1}{8\,ac-2\,{b}^{2}} \left ( \left ( -2\,{a}^{2}x-ab \right ) \sqrt {{\frac {-4\,ac+{b}^{2}}{{a}^{2}}}}+4\,ac-{b}^{2} \right ) })} \right \} \]