\[ \text {a0} y(x)+\text {a1} y'(x)+\text {a2} y''(x)+y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.0054836 (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 = 0.03 (sec), leaf count = 590
\[\left \{y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {\left (\frac {\left (-8 \mathit {a2}^{3}+36 \mathit {a1} \mathit {a2} -108 \mathit {a0} +12 \sqrt {12 \mathit {a0} \,\mathit {a2}^{3}-3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a1} \mathit {a2} \mathit {a0} +12 \mathit {a1}^{3}+81 \mathit {a0}^{2}}\right )^{\frac {1}{3}} \mathit {a2}}{3}+\left (\frac {i \sqrt {3}}{12}+\frac {1}{12}\right ) \left (-8 \mathit {a2}^{3}+36 \mathit {a1} \mathit {a2} -108 \mathit {a0} +12 \sqrt {12 \mathit {a0} \,\mathit {a2}^{3}-3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a1} \mathit {a2} \mathit {a0} +12 \mathit {a1}^{3}+81 \mathit {a0}^{2}}\right )^{\frac {2}{3}}+\left (i \sqrt {3}-1\right ) \left (-\frac {\mathit {a2}^{2}}{3}+\mathit {a1} \right )\right ) x}{\left (-8 \mathit {a2}^{3}+36 \mathit {a1} \mathit {a2} -108 \mathit {a0} +12 \sqrt {12 \mathit {a0} \,\mathit {a2}^{3}-3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a1} \mathit {a2} \mathit {a0} +12 \mathit {a1}^{3}+81 \mathit {a0}^{2}}\right )^{\frac {1}{3}}}}+c_{2} {\mathrm e}^{\frac {\left (-4 i \sqrt {3}\, \mathit {a2}^{2}-4 \mathit {a2}^{2}+12 i \sqrt {3}\, \mathit {a1} +12 \mathit {a1} -4 \left (-8 \mathit {a2}^{3}+36 \mathit {a1} \mathit {a2} -108 \mathit {a0} +12 \sqrt {12 \mathit {a0} \,\mathit {a2}^{3}-3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a1} \mathit {a2} \mathit {a0} +12 \mathit {a1}^{3}+81 \mathit {a0}^{2}}\right )^{\frac {1}{3}} \mathit {a2} +i \left (-8 \mathit {a2}^{3}+36 \mathit {a1} \mathit {a2} -108 \mathit {a0} +12 \sqrt {12 \mathit {a0} \,\mathit {a2}^{3}-3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a1} \mathit {a2} \mathit {a0} +12 \mathit {a1}^{3}+81 \mathit {a0}^{2}}\right )^{\frac {2}{3}} \sqrt {3}-\left (-8 \mathit {a2}^{3}+36 \mathit {a1} \mathit {a2} -108 \mathit {a0} +12 \sqrt {12 \mathit {a0} \,\mathit {a2}^{3}-3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a1} \mathit {a2} \mathit {a0} +12 \mathit {a1}^{3}+81 \mathit {a0}^{2}}\right )^{\frac {2}{3}}\right ) x}{12 \left (-8 \mathit {a2}^{3}+36 \mathit {a1} \mathit {a2} -108 \mathit {a0} +12 \sqrt {12 \mathit {a0} \,\mathit {a2}^{3}-3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a1} \mathit {a2} \mathit {a0} +12 \mathit {a1}^{3}+81 \mathit {a0}^{2}}\right )^{\frac {1}{3}}}}+c_{3} {\mathrm e}^{\frac {\left (4 \mathit {a2}^{2}-12 \mathit {a1} -2 \left (-8 \mathit {a2}^{3}+36 \mathit {a1} \mathit {a2} -108 \mathit {a0} +12 \sqrt {12 \mathit {a0} \,\mathit {a2}^{3}-3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a1} \mathit {a2} \mathit {a0} +12 \mathit {a1}^{3}+81 \mathit {a0}^{2}}\right )^{\frac {1}{3}} \mathit {a2} +\left (-8 \mathit {a2}^{3}+36 \mathit {a1} \mathit {a2} -108 \mathit {a0} +12 \sqrt {12 \mathit {a0} \,\mathit {a2}^{3}-3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a1} \mathit {a2} \mathit {a0} +12 \mathit {a1}^{3}+81 \mathit {a0}^{2}}\right )^{\frac {2}{3}}\right ) x}{6 \left (-8 \mathit {a2}^{3}+36 \mathit {a1} \mathit {a2} -108 \mathit {a0} +12 \sqrt {12 \mathit {a0} \,\mathit {a2}^{3}-3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a1} \mathit {a2} \mathit {a0} +12 \mathit {a1}^{3}+81 \mathit {a0}^{2}}\right )^{\frac {1}{3}}}}\right \}\]