\[ y(x) (\text {a0} x+\text {b0})+(\text {a1} x+\text {b1}) y'(x)+(\text {a2} x+\text {b2}) y''(x)=0 \] ✓ Mathematica : cpu = 0.262366 (sec), leaf count = 386
\[\left \{\left \{y(x)\to c_1 U\left (-\frac {\text {b2} \text {a1}^2-\text {a2} \text {b1} \text {a1}-\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {b2} \text {a1}+2 \text {a2}^2 \text {b0}+\text {a2} \sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {b1}-2 \text {a0} \text {a2} \text {b2}-2 \text {a2}^2 \sqrt {\text {a1}^2-4 \text {a0} \text {a2}}}{2 \text {a2}^2 \sqrt {\text {a1}^2-4 \text {a0} \text {a2}}},\frac {\text {a2}^2-\text {b1} \text {a2}+\text {a1} \text {b2}}{\text {a2}^2}+1,\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {b2}}{\text {a2}^2}+\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} x}{\text {a2}}\right ) \exp \left (\frac {2 \left (\frac {\text {a1} \text {b2}}{\text {a2}}+\text {a2}-\text {b1}\right ) \log (\text {a2} x+\text {b2})-x \left (\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}+\text {a1}\right )}{2 \text {a2}}\right )+c_2 L_{\frac {\text {b2} \text {a1}^2-\text {a2} \text {b1} \text {a1}-\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {b2} \text {a1}+2 \text {a2}^2 \text {b0}+\text {a2} \sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {b1}-2 \text {a0} \text {a2} \text {b2}-2 \text {a2}^2 \sqrt {\text {a1}^2-4 \text {a0} \text {a2}}}{2 \text {a2}^2 \sqrt {\text {a1}^2-4 \text {a0} \text {a2}}}}^{\frac {\text {a2}^2-\text {b1} \text {a2}+\text {a1} \text {b2}}{\text {a2}^2}}\left (\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {b2}}{\text {a2}^2}+\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} x}{\text {a2}}\right ) \exp \left (\frac {2 \left (\frac {\text {a1} \text {b2}}{\text {a2}}+\text {a2}-\text {b1}\right ) \log (\text {a2} x+\text {b2})-x \left (\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}+\text {a1}\right )}{2 \text {a2}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.492 (sec), leaf count = 248
\[ \left \{ y \left ( x \right ) = \left ( {\it a2}\,x+{\it b2} \right ) ^{{\frac {{\it a1}\,{\it b2}+{{\it a2}}^{2}-{\it a2}\,{\it b1}}{{{\it a2}}^{2}}}}{{\rm e}^{-{\frac {x}{2\,{\it a2}} \left ( \sqrt {-4\,{\it a0}\,{\it a2}+{{\it a1}}^{2}}+{\it a1} \right ) }}} \left ( {{\sl U}\left ({\frac {1}{2\,{{\it a2}}^{2}} \left ( \left ( {\it a1}\,{\it b2}+2\,{{\it a2}}^{2}-{\it a2}\,{\it b1} \right ) \sqrt {-4\,{\it a0}\,{\it a2}+{{\it a1}}^{2}}-2\,{{\it a2}}^{2}{\it b0}+ \left ( 2\,{\it a0}\,{\it b2}+{\it a1}\,{\it b1} \right ) {\it a2}-{{\it a1}}^{2}{\it b2} \right ) {\frac {1}{\sqrt {-4\,{\it a0}\,{\it a2}+{{\it a1}}^{2}}}}},\,{\frac {{\it a1}\,{\it b2}+2\,{{\it a2}}^{2}-{\it a2}\,{\it b1}}{{{\it a2}}^{2}}},\,{\frac {{\it a2}\,x+{\it b2}}{{{\it a2}}^{2}}\sqrt {-4\,{\it a0}\,{\it a2}+{{\it a1}}^{2}}}\right )}{\it \_C2}+{{\sl M}\left ({\frac {1}{2\,{{\it a2}}^{2}} \left ( \left ( {\it a1}\,{\it b2}+2\,{{\it a2}}^{2}-{\it a2}\,{\it b1} \right ) \sqrt {-4\,{\it a0}\,{\it a2}+{{\it a1}}^{2}}-2\,{{\it a2}}^{2}{\it b0}+ \left ( 2\,{\it a0}\,{\it b2}+{\it a1}\,{\it b1} \right ) {\it a2}-{{\it a1}}^{2}{\it b2} \right ) {\frac {1}{\sqrt {-4\,{\it a0}\,{\it a2}+{{\it a1}}^{2}}}}},\,{\frac {{\it a1}\,{\it b2}+2\,{{\it a2}}^{2}-{\it a2}\,{\it b1}}{{{\it a2}}^{2}}},\,{\frac {{\it a2}\,x+{\it b2}}{{{\it a2}}^{2}}\sqrt {-4\,{\it a0}\,{\it a2}+{{\it a1}}^{2}}}\right )}{\it \_C1} \right ) \right \} \]