\[ \text {a0} y(x)+\text {a1} y'(x)+\text {a2} y''(x)+y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.00651583 (sec), leaf count = 84
\[\left \{\left \{y(x)\to c_1 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\& ,1\right ]}+c_2 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\& ,2\right ]}+c_3 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\& ,3\right ]}\right \}\right \}\]
✓ Maple : cpu = 0.029 (sec), leaf count = 590
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{x \left ( \left ( {\frac {i}{12}}\sqrt {3}+{\frac {1}{12}} \right ) \left ( 36\,{\it a1}\,{\it a2}-108\,{\it a0}-8\,{{\it a2}}^{3}+12\,\sqrt {12\,{\it a0}\,{{\it a2}}^{3}-3\,{{\it a1}}^{2}{{\it a2}}^{2}-54\,{\it a1}\,{\it a2}\,{\it a0}+12\,{{\it a1}}^{3}+81\,{{\it a0}}^{2}} \right ) ^{{\frac {2}{3}}}+{\frac {{\it a2}}{3}\sqrt [3]{36\,{\it a1}\,{\it a2}-108\,{\it a0}-8\,{{\it a2}}^{3}+12\,\sqrt {12\,{\it a0}\,{{\it a2}}^{3}-3\,{{\it a1}}^{2}{{\it a2}}^{2}-54\,{\it a1}\,{\it a2}\,{\it a0}+12\,{{\it a1}}^{3}+81\,{{\it a0}}^{2}}}}+ \left ( {\it a1}-{\frac {{{\it a2}}^{2}}{3}} \right ) \left ( i\sqrt {3}-1 \right ) \right ) {\frac {1}{\sqrt [3]{36\,{\it a1}\,{\it a2}-108\,{\it a0}-8\,{{\it a2}}^{3}+12\,\sqrt {12\,{\it a0}\,{{\it a2}}^{3}-3\,{{\it a1}}^{2}{{\it a2}}^{2}-54\,{\it a1}\,{\it a2}\,{\it a0}+12\,{{\it a1}}^{3}+81\,{{\it a0}}^{2}}}}}}}}+{\it \_C2}\,{{\rm e}^{{\frac {x}{12} \left ( i \left ( 36\,{\it a1}\,{\it a2}-108\,{\it a0}-8\,{{\it a2}}^{3}+12\,\sqrt {12\,{\it a0}\,{{\it a2}}^{3}-3\,{{\it a1}}^{2}{{\it a2}}^{2}-54\,{\it a1}\,{\it a2}\,{\it a0}+12\,{{\it a1}}^{3}+81\,{{\it a0}}^{2}} \right ) ^{{\frac {2}{3}}}\sqrt {3}-4\,i\sqrt {3}{{\it a2}}^{2}+12\,i\sqrt {3}{\it a1}- \left ( 36\,{\it a1}\,{\it a2}-108\,{\it a0}-8\,{{\it a2}}^{3}+12\,\sqrt {12\,{\it a0}\,{{\it a2}}^{3}-3\,{{\it a1}}^{2}{{\it a2}}^{2}-54\,{\it a1}\,{\it a2}\,{\it a0}+12\,{{\it a1}}^{3}+81\,{{\it a0}}^{2}} \right ) ^{{\frac {2}{3}}}-4\,{\it a2}\,\sqrt [3]{36\,{\it a1}\,{\it a2}-108\,{\it a0}-8\,{{\it a2}}^{3}+12\,\sqrt {12\,{\it a0}\,{{\it a2}}^{3}-3\,{{\it a1}}^{2}{{\it a2}}^{2}-54\,{\it a1}\,{\it a2}\,{\it a0}+12\,{{\it a1}}^{3}+81\,{{\it a0}}^{2}}}-4\,{{\it a2}}^{2}+12\,{\it a1} \right ) {\frac {1}{\sqrt [3]{36\,{\it a1}\,{\it a2}-108\,{\it a0}-8\,{{\it a2}}^{3}+12\,\sqrt {12\,{\it a0}\,{{\it a2}}^{3}-3\,{{\it a1}}^{2}{{\it a2}}^{2}-54\,{\it a1}\,{\it a2}\,{\it a0}+12\,{{\it a1}}^{3}+81\,{{\it a0}}^{2}}}}}}}}+{\it \_C3}\,{{\rm e}^{{\frac {x}{6} \left ( \left ( 36\,{\it a1}\,{\it a2}-108\,{\it a0}-8\,{{\it a2}}^{3}+12\,\sqrt {12\,{\it a0}\,{{\it a2}}^{3}-3\,{{\it a1}}^{2}{{\it a2}}^{2}-54\,{\it a1}\,{\it a2}\,{\it a0}+12\,{{\it a1}}^{3}+81\,{{\it a0}}^{2}} \right ) ^{{\frac {2}{3}}}-2\,{\it a2}\,\sqrt [3]{36\,{\it a1}\,{\it a2}-108\,{\it a0}-8\,{{\it a2}}^{3}+12\,\sqrt {12\,{\it a0}\,{{\it a2}}^{3}-3\,{{\it a1}}^{2}{{\it a2}}^{2}-54\,{\it a1}\,{\it a2}\,{\it a0}+12\,{{\it a1}}^{3}+81\,{{\it a0}}^{2}}}+4\,{{\it a2}}^{2}-12\,{\it a1} \right ) {\frac {1}{\sqrt [3]{36\,{\it a1}\,{\it a2}-108\,{\it a0}-8\,{{\it a2}}^{3}+12\,\sqrt {12\,{\it a0}\,{{\it a2}}^{3}-3\,{{\it a1}}^{2}{{\it a2}}^{2}-54\,{\it a1}\,{\it a2}\,{\it a0}+12\,{{\it a1}}^{3}+81\,{{\it a0}}^{2}}}}}}}} \right \} \]