\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( ax+b \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) x+ \left ( {\it a1}\,{x}^{2}+{\it b1}\,x+{\it c1} \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.123516 (sec), leaf count = 294 \[ \left \{\left \{y(x)\to c_1 U\left (-\frac {-a b+2 \text {b1}-\sqrt {a^2-4 \text {a1}}-\sqrt {a^2-4 \text {a1}} \sqrt {b^2-2 b-4 \text {c1}+1}}{2 \sqrt {a^2-4 \text {a1}}},\sqrt {b^2-2 b-4 \text {c1}+1}+1,\sqrt {a^2-4 \text {a1}} x\right ) \exp \left (\frac {1}{2} \left (x \left (-\left (\sqrt {a^2-4 \text {a1}}+a\right )\right )-\left (-\sqrt {b^2-2 b-4 \text {c1}+1}+b-1\right ) \log (x)\right )\right )+c_2 L_{\frac {-\sqrt {a^2-4 \text {a1}} \sqrt {b^2-2 b-4 \text {c1}+1}-\sqrt {a^2-4 \text {a1}}-a b+2 \text {b1}}{2 \sqrt {a^2-4 \text {a1}}}}^{\sqrt {b^2-2 b-4 \text {c1}+1}}\left (x \sqrt {a^2-4 \text {a1}}\right ) \exp \left (\frac {1}{2} \left (x \left (-\left (\sqrt {a^2-4 \text {a1}}+a\right )\right )-\left (-\sqrt {b^2-2 b-4 \text {c1}+1}+b-1\right ) \log (x)\right )\right )\right \}\right \} \]
Maple: cpu = 0.156 (sec), leaf count = 119 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {ax}{2}}}}{ x}^{-{\frac {b}{2}}}{{\sl M}_{-{\frac {ab-2\,{\it b1}}{2}{\frac {1}{ \sqrt {{a}^{2}-4\,{\it a1}}}}},\,{\frac {1}{2}\sqrt {{b}^{2}-2\,b-4\,{ \it c1}+1}}}\left (\sqrt {{a}^{2}-4\,{\it a1}}x\right )}+{\it \_C2}\,{ {\rm e}^{-{\frac {ax}{2}}}}{x}^{-{\frac {b}{2}}}{{\sl W}_{-{\frac {ab- 2\,{\it b1}}{2}{\frac {1}{\sqrt {{a}^{2}-4\,{\it a1}}}}},\,{\frac {1}{ 2}\sqrt {{b}^{2}-2\,b-4\,{\it c1}+1}}}\left (\sqrt {{a}^{2}-4\,{\it a1} }x\right )} \right \} \]