7.12   ODE No. 1585

$$\boxed{{\displaystyle x(a\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+b\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+c\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+e\mathit{d}\mathit{4}\mathit{y}\left(x\right))y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.247031 (sec), leaf count = 214 $$\{\{y(x)\to 0\},\{y(x)\to \frac{c_1{e}^{x\text{Root}[{\mathrm{\#}\text{1}}^3+\frac{{\mathrm{\#}\text{1}}^{2}c}{e}+\frac{\mathrm{\#}\text{1}b}{e}+\frac{a}{e}\mathrm{\&},1]}}{\text{Root}[{\mathrm{\#}\text{1}}^3+\frac{{\mathrm{\#}\text{1}}^{2}c}{e}+\frac{\mathrm{\#}\text{1}b}{e}+\frac{a}{e}\mathrm{\&},1]}+\frac{c_2{e}^{x\text{Root}[{\mathrm{\#}\text{1}}^3+\frac{{\mathrm{\#}\text{1}}^{2}c}{e}+\frac{\mathrm{\#}\text{1}b}{e}+\frac{a}{e}\mathrm{\&},2]}}{\text{Root}[{\mathrm{\#}\text{1}}^3+\frac{{\mathrm{\#}\text{1}}^{2}c}{e}+\frac{\mathrm{\#}\text{1}b}{e}+\frac{a}{e}\mathrm{\&},2]}+\frac{c_3{e}^{x\text{Root}[{\mathrm{\#}\text{1}}^3+\frac{{\mathrm{\#}\text{1}}^{2}c}{e}+\frac{\mathrm{\#}\text{1}b}{e}+\frac{a}{e}\mathrm{\&},3]}}{\text{Root}[{\mathrm{\#}\text{1}}^3+\frac{{\mathrm{\#}\text{1}}^{2}c}{e}+\frac{\mathrm{\#}\text{1}b}{e}+\frac{a}{e}\mathrm{\&},3]}+c_4\}\}$$

Maple: cpu = 0.016 (sec), leaf count = 806 $$\{y\left(x\right)=0,y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{x}{12e}(i{(12\sqrt{3}\sqrt{27a^2{e}^2-18abce+4a{c}^3+4b^{3}e-b^2{c}^2}e-108a{e}^2+36bce-8c^3)}^{\frac{2}{3}}\sqrt{3}+12i\sqrt{3}be-4i\sqrt{3}{c}^2+{(12\sqrt{3}\sqrt{27a^2{e}^2-18abce+4a{c}^3+4b^{3}e-b^2{c}^2}e-108a{e}^2+36bce-8c^3)}^{\frac{2}{3}}+4c\sqrt[3]{12\sqrt{3}\sqrt{27a^2{e}^2-18abce+4a{c}^3+4b^{3}e-b^2{c}^2}e-108a{e}^2+36bce-8c^3}-12be+4c^2)\frac{1}{\sqrt[3]{12\sqrt{3}\sqrt{27a^2{e}^2-18abce+4a{c}^3+4b^{3}e-b^2{c}^2}e-108a{e}^2+36bce-8c^3}}}+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{\frac{x}{12e}(i{(12\sqrt{3}\sqrt{27a^2{e}^2-18abce+4a{c}^3+4b^{3}e-b^2{c}^2}e-108a{e}^2+36bce-8c^3)}^{\frac{2}{3}}\sqrt{3}+12i\sqrt{3}be-4i\sqrt{3}{c}^2-{(12\sqrt{3}\sqrt{27a^2{e}^2-18abce+4a{c}^3+4b^{3}e-b^2{c}^2}e-108a{e}^2+36bce-8c^3)}^{\frac{2}{3}}-4c\sqrt[3]{12\sqrt{3}\sqrt{27a^2{e}^2-18abce+4a{c}^3+4b^{3}e-b^2{c}^2}e-108a{e}^2+36bce-8c^3}+12be-4c^2)\frac{1}{\sqrt[3]{12\sqrt{3}\sqrt{27a^2{e}^2-18abce+4a{c}^3+4b^{3}e-b^2{c}^2}e-108a{e}^2+36bce-8c^3}}}+\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{\frac{x}{6e}({(12\sqrt{3}\sqrt{27a^2{e}^2-18abce+4a{c}^3+4b^{3}e-b^2{c}^2}e-108a{e}^2+36bce-8c^3)}^{\frac{2}{3}}-2c\sqrt[3]{12\sqrt{3}\sqrt{27a^2{e}^2-18abce+4a{c}^3+4b^{3}e-b^2{c}^2}e-108a{e}^2+36bce-8c^3}-12be+4c^2)\frac{1}{\sqrt[3]{12\sqrt{3}\sqrt{27a^2{e}^2-18abce+4a{c}^3+4b^{3}e-b^2{c}^2}e-108a{e}^2+36bce-8c^3}}}\}$$