\[ x (a x+b) y'(x)+y(x) \left (\text {a1} x^2+\text {b1} x+\text {c1}\right )+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.134997 (sec), leaf count = 223
\[\left \{\left \{y(x)\to e^{-\frac {1}{2} x \left (\sqrt {a^2-4 \text {a1}}+a\right )} x^{\frac {1}{2} \left (\sqrt {b^2-2 b-4 \text {c1}+1}-b+1\right )} \left (c_1 U\left (\frac {a b-2 \text {b1}+\sqrt {a^2-4 \text {a1}} \left (\sqrt {b^2-2 b-4 \text {c1}+1}+1\right )}{2 \sqrt {a^2-4 \text {a1}}},\sqrt {b^2-2 b-4 \text {c1}+1}+1,\sqrt {a^2-4 \text {a1}} x\right )+c_2 L_{\frac {-a b+2 \text {b1}-\sqrt {a^2-4 \text {a1}} \left (\sqrt {b^2-2 b-4 \text {c1}+1}+1\right )}{2 \sqrt {a^2-4 \text {a1}}}}^{\sqrt {b^2-2 b-4 \text {c1}+1}}\left (\sqrt {a^2-4 \text {a1}} x\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.232 (sec), leaf count = 110
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {ax}{2}}}}{x}^{-{\frac {b}{2}}} \left ( {{\sl M}_{-{\frac {ab-2\,{\it b1}}{2}{\frac {1}{\sqrt {{a}^{2}-4\,{\it a1}}}}},\,{\frac {1}{2}\sqrt {{b}^{2}-2\,b-4\,{\it c1}+1}}}\left (\sqrt {{a}^{2}-4\,{\it a1}}x\right )}{\it \_C1}+{{\sl W}_{-{\frac {ab-2\,{\it b1}}{2}{\frac {1}{\sqrt {{a}^{2}-4\,{\it a1}}}}},\,{\frac {1}{2}\sqrt {{b}^{2}-2\,b-4\,{\it c1}+1}}}\left (\sqrt {{a}^{2}-4\,{\it a1}}x\right )}{\it \_C2} \right ) \right \} \]