\[ (a x+b) y'(x)+c y(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.138515 (sec), leaf count = 243
\[\left \{\left \{y(x)\to -i^{-\sqrt {a^2-2 a-4 c+1}+a+1} b^{\frac {1}{2} \left (-\sqrt {a^2-2 a-4 c+1}+a-1\right )} \left (\frac {1}{x}\right )^{\frac {1}{2} \left (-\sqrt {a^2-2 a-4 c+1}+a-1\right )} \left (c_1 \, _1F_1\left (\frac {1}{2} \left (a-\sqrt {a^2-2 a-4 c+1}-1\right );1-\sqrt {a^2-2 a-4 c+1};\frac {b}{x}\right )+c_2 i^{2 \sqrt {a^2-2 a-4 c+1}} b^{\sqrt {a^2-2 a-4 c+1}} \left (\frac {1}{x}\right )^{\sqrt {a^2-2 a-4 c+1}} \, _1F_1\left (\frac {1}{2} \left (a+\sqrt {a^2-2 a-4 c+1}-1\right );\sqrt {a^2-2 a-4 c+1}+1;\frac {b}{x}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.266 (sec), leaf count = 114
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}-{\frac {a}{2}}+{\frac {1}{2}}} \left ( {{\sl U}\left (-{\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}},\,1+\sqrt {{a}^{2}-2\,a-4\,c+1},\,{\frac {b}{x}}\right )}{\it \_C2}+{{\sl M}\left (-{\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}},\,1+\sqrt {{a}^{2}-2\,a-4\,c+1},\,{\frac {b}{x}}\right )}{\it \_C1} \right ) \right \} \]