\[ (a x+b) y'(x)+c y(x)+(x-1) x y''(x)=0 \] ✓ Mathematica : cpu = 0.121228 (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 = 0.296 (sec), leaf count = 110
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_2$F$_1$}(-{\frac {1}{2}}-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}},-{\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}};\,-b;\,x)}+{\it \_C2}\,{x}^{b+1}{\mbox {$_2$F$_1$}({\frac {1}{2}}-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}}+b,{\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}}+b;\,b+2;\,x)} \right \} \]