2.1585   ODE No. 1585

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

$$xy(x)(a{y}^{\prime }(x)+b{y}^{″}(x)+c{y}^{(3)}(x)+e{y}^{(4)}(x))=0$$ ✓ Mathematica : cpu = 0.211034 (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 = 0.063 (sec), leaf count = 806

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