5.19   ODE No. 1467

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+\mathit{a}\mathit{2}\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+\mathit{a}\mathit{1}\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+\mathit{a}\mathit{0}y\left(x\right)=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 0.005001 (sec), leaf count = 84 $$\left\{\{y(x)\to c_1{e}^{x\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},1]}+c_2{e}^{x\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},2]}+c_3{e}^{x\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2\text{a2}+\mathrm{\#}\text{1}\text{a1}+\text{a0}\mathrm{\&},3]}\}\right\}$$

Maple: cpu = 0.015 (sec), leaf count = 644 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{x}{12}(i{(36\mathit{a}\mathit{1}\mathit{a}\mathit{2}-108\mathit{a}\mathit{0}-8{\mathit{a}\mathit{2}}^3+12\sqrt{12\mathit{a}\mathit{0}{\mathit{a}\mathit{2}}^3-3{\mathit{a}\mathit{1}}^2{\mathit{a}\mathit{2}}^2-54\mathit{a}\mathit{1}\mathit{a}\mathit{2}\mathit{a}\mathit{0}+12{\mathit{a}\mathit{1}}^3+81{\mathit{a}\mathit{0}}^2})}^{\frac{2}{3}}\sqrt{3}-4i\sqrt{3}{\mathit{a}\mathit{2}}^2+12i\sqrt{3}\mathit{a}\mathit{1}+{(36\mathit{a}\mathit{1}\mathit{a}\mathit{2}-108\mathit{a}\mathit{0}-8{\mathit{a}\mathit{2}}^3+12\sqrt{12\mathit{a}\mathit{0}{\mathit{a}\mathit{2}}^3-3{\mathit{a}\mathit{1}}^2{\mathit{a}\mathit{2}}^2-54\mathit{a}\mathit{1}\mathit{a}\mathit{2}\mathit{a}\mathit{0}+12{\mathit{a}\mathit{1}}^3+81{\mathit{a}\mathit{0}}^2})}^{\frac{2}{3}}+4\mathit{a}\mathit{2}\sqrt[3]{36\mathit{a}\mathit{1}\mathit{a}\mathit{2}-108\mathit{a}\mathit{0}-8{\mathit{a}\mathit{2}}^3+12\sqrt{12\mathit{a}\mathit{0}{\mathit{a}\mathit{2}}^3-3{\mathit{a}\mathit{1}}^2{\mathit{a}\mathit{2}}^2-54\mathit{a}\mathit{1}\mathit{a}\mathit{2}\mathit{a}\mathit{0}+12{\mathit{a}\mathit{1}}^3+81{\mathit{a}\mathit{0}}^2}}+4{\mathit{a}\mathit{2}}^2-12\mathit{a}\mathit{1})\frac{1}{\sqrt[3]{36\mathit{a}\mathit{1}\mathit{a}\mathit{2}-108\mathit{a}\mathit{0}-8{\mathit{a}\mathit{2}}^3+12\sqrt{12\mathit{a}\mathit{0}{\mathit{a}\mathit{2}}^3-3{\mathit{a}\mathit{1}}^2{\mathit{a}\mathit{2}}^2-54\mathit{a}\mathit{1}\mathit{a}\mathit{2}\mathit{a}\mathit{0}+12{\mathit{a}\mathit{1}}^3+81{\mathit{a}\mathit{0}}^2}}}}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\frac{x}{12}(i{(36\mathit{a}\mathit{1}\mathit{a}\mathit{2}-108\mathit{a}\mathit{0}-8{\mathit{a}\mathit{2}}^3+12\sqrt{12\mathit{a}\mathit{0}{\mathit{a}\mathit{2}}^3-3{\mathit{a}\mathit{1}}^2{\mathit{a}\mathit{2}}^2-54\mathit{a}\mathit{1}\mathit{a}\mathit{2}\mathit{a}\mathit{0}+12{\mathit{a}\mathit{1}}^3+81{\mathit{a}\mathit{0}}^2})}^{\frac{2}{3}}\sqrt{3}-4i\sqrt{3}{\mathit{a}\mathit{2}}^2+12i\sqrt{3}\mathit{a}\mathit{1}-{(36\mathit{a}\mathit{1}\mathit{a}\mathit{2}-108\mathit{a}\mathit{0}-8{\mathit{a}\mathit{2}}^3+12\sqrt{12\mathit{a}\mathit{0}{\mathit{a}\mathit{2}}^3-3{\mathit{a}\mathit{1}}^2{\mathit{a}\mathit{2}}^2-54\mathit{a}\mathit{1}\mathit{a}\mathit{2}\mathit{a}\mathit{0}+12{\mathit{a}\mathit{1}}^3+81{\mathit{a}\mathit{0}}^2})}^{\frac{2}{3}}-4\mathit{a}\mathit{2}\sqrt[3]{36\mathit{a}\mathit{1}\mathit{a}\mathit{2}-108\mathit{a}\mathit{0}-8{\mathit{a}\mathit{2}}^3+12\sqrt{12\mathit{a}\mathit{0}{\mathit{a}\mathit{2}}^3-3{\mathit{a}\mathit{1}}^2{\mathit{a}\mathit{2}}^2-54\mathit{a}\mathit{1}\mathit{a}\mathit{2}\mathit{a}\mathit{0}+12{\mathit{a}\mathit{1}}^3+81{\mathit{a}\mathit{0}}^2}}-4{\mathit{a}\mathit{2}}^2+12\mathit{a}\mathit{1})\frac{1}{\sqrt[3]{36\mathit{a}\mathit{1}\mathit{a}\mathit{2}-108\mathit{a}\mathit{0}-8{\mathit{a}\mathit{2}}^3+12\sqrt{12\mathit{a}\mathit{0}{\mathit{a}\mathit{2}}^3-3{\mathit{a}\mathit{1}}^2{\mathit{a}\mathit{2}}^2-54\mathit{a}\mathit{1}\mathit{a}\mathit{2}\mathit{a}\mathit{0}+12{\mathit{a}\mathit{1}}^3+81{\mathit{a}\mathit{0}}^2}}}}+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{\frac{x}{6}({(36\mathit{a}\mathit{1}\mathit{a}\mathit{2}-108\mathit{a}\mathit{0}-8{\mathit{a}\mathit{2}}^3+12\sqrt{12\mathit{a}\mathit{0}{\mathit{a}\mathit{2}}^3-3{\mathit{a}\mathit{1}}^2{\mathit{a}\mathit{2}}^2-54\mathit{a}\mathit{1}\mathit{a}\mathit{2}\mathit{a}\mathit{0}+12{\mathit{a}\mathit{1}}^3+81{\mathit{a}\mathit{0}}^2})}^{\frac{2}{3}}-2\mathit{a}\mathit{2}\sqrt[3]{36\mathit{a}\mathit{1}\mathit{a}\mathit{2}-108\mathit{a}\mathit{0}-8{\mathit{a}\mathit{2}}^3+12\sqrt{12\mathit{a}\mathit{0}{\mathit{a}\mathit{2}}^3-3{\mathit{a}\mathit{1}}^2{\mathit{a}\mathit{2}}^2-54\mathit{a}\mathit{1}\mathit{a}\mathit{2}\mathit{a}\mathit{0}+12{\mathit{a}\mathit{1}}^3+81{\mathit{a}\mathit{0}}^2}}+4{\mathit{a}\mathit{2}}^2-12\mathit{a}\mathit{1})\frac{1}{\sqrt[3]{36\mathit{a}\mathit{1}\mathit{a}\mathit{2}-108\mathit{a}\mathit{0}-8{\mathit{a}\mathit{2}}^3+12\sqrt{12\mathit{a}\mathit{0}{\mathit{a}\mathit{2}}^3-3{\mathit{a}\mathit{1}}^2{\mathit{a}\mathit{2}}^2-54\mathit{a}\mathit{1}\mathit{a}\mathit{2}\mathit{a}\mathit{0}+12{\mathit{a}\mathit{1}}^3+81{\mathit{a}\mathit{0}}^2}}}}\}$$