\[ y(x) \left (\text {a0} x^2+\text {b0} x+\text {c0}\right )+\left (\text {a1} x^2+\text {b1} x\right ) y'(x)+\text {a2} x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.557298 (sec), leaf count = 272
\[\left \{\left \{y(x)\to e^{-\frac {x \left (\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}+\text {a1}\right )}{2 \text {a2}}} x^{\frac {\sqrt {\text {a2}^2-2 \text {a2} (\text {b1}+2 \text {c0})+\text {b1}^2}+\text {a2}-\text {b1}}{2 \text {a2}}} \left (c_1 U\left (\frac {-\frac {2 \text {b0} \text {a2}}{\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}}+\text {a2}+\frac {\text {a1} \text {b1}}{\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}}+\sqrt {\text {a2}^2-2 (\text {b1}+2 \text {c0}) \text {a2}+\text {b1}^2}}{2 \text {a2}},\frac {\text {a2}+\sqrt {\text {a2}^2-2 (\text {b1}+2 \text {c0}) \text {a2}+\text {b1}^2}}{\text {a2}},\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} x}{\text {a2}}\right )+c_2 L_{-\frac {-\frac {2 \text {b0} \text {a2}}{\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}}+\text {a2}+\frac {\text {a1} \text {b1}}{\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}}+\sqrt {\text {a2}^2-2 (\text {b1}+2 \text {c0}) \text {a2}+\text {b1}^2}}{2 \text {a2}}}^{\frac {\sqrt {\text {a2}^2-2 (\text {b1}+2 \text {c0}) \text {a2}+\text {b1}^2}}{\text {a2}}}\left (\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} x}{\text {a2}}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.444 (sec), leaf count = 150
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {{\it b1}}{2\,{\it a2}}}}{{\rm e}^{-{\frac {{\it a1}\,x}{2\,{\it a2}}}}} \left ( {{\sl M}_{-{\frac {{\it a1}\,{\it b1}-2\,{\it a2}\,{\it b0}}{2\,{\it a2}}{\frac {1}{\sqrt {-4\,{\it a0}\,{\it a2}+{{\it a1}}^{2}}}}},\,{\frac {1}{2\,{\it a2}}\sqrt {{{\it a2}}^{2}+ \left ( -2\,{\it b1}-4\,{\it c0} \right ) {\it a2}+{{\it b1}}^{2}}}}\left ({\frac {x}{{\it a2}}\sqrt {-4\,{\it a0}\,{\it a2}+{{\it a1}}^{2}}}\right )}{\it \_C1}+{{\sl W}_{-{\frac {{\it a1}\,{\it b1}-2\,{\it a2}\,{\it b0}}{2\,{\it a2}}{\frac {1}{\sqrt {-4\,{\it a0}\,{\it a2}+{{\it a1}}^{2}}}}},\,{\frac {1}{2\,{\it a2}}\sqrt {{{\it a2}}^{2}+ \left ( -2\,{\it b1}-4\,{\it c0} \right ) {\it a2}+{{\it b1}}^{2}}}}\left ({\frac {x}{{\it a2}}\sqrt {-4\,{\it a0}\,{\it a2}+{{\it a1}}^{2}}}\right )}{\it \_C2} \right ) \right \} \]