3.327   ODE No. 327

$$\boxed{{\displaystyle (x{\left(y\left(x\right)\right)}^4+2x^2{\left(y\left(x\right)\right)}^3+2y\left(x\right)+x)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+{\left(y\left(x\right)\right)}^5+y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.384549 (sec), leaf count = 669 $$\{\{y(x)\to \frac{\sqrt[3]{9c_1^2{x}^2+3\sqrt{3}\sqrt{-4c_1^3{x}^6-c_1^4{x}^4+18c_1^2{x}^4+4c_1^3{x}^2+27x^4}+2c_1^3+27x^2}}{3\sqrt[3]{2}x}-\frac{\sqrt[3]{2}(-3c_1{x}^2-c_1^2)}{3x\sqrt[3]{9c_1^2{x}^2+3\sqrt{3}\sqrt{-4c_1^3{x}^6-c_1^4{x}^4+18c_1^2{x}^4+4c_1^3{x}^2+27x^4}+2c_1^3+27x^2}}+\frac{c_1}{3x}\},\{y(x)\to -\frac{(1-i\sqrt{3})\sqrt[3]{9c_1^2{x}^2+3\sqrt{3}\sqrt{-4c_1^3{x}^6-c_1^4{x}^4+18c_1^2{x}^4+4c_1^3{x}^2+27x^4}+2c_1^3+27x^2}}{6\sqrt[3]{2}x}+\frac{(1+i\sqrt{3})(-3c_1{x}^2-c_1^2)}{32^{2/3}x\sqrt[3]{9c_1^2{x}^2+3\sqrt{3}\sqrt{-4c_1^3{x}^6-c_1^4{x}^4+18c_1^2{x}^4+4c_1^3{x}^2+27x^4}+2c_1^3+27x^2}}+\frac{c_1}{3x}\},\{y(x)\to -\frac{(1+i\sqrt{3})\sqrt[3]{9c_1^2{x}^2+3\sqrt{3}\sqrt{-4c_1^3{x}^6-c_1^4{x}^4+18c_1^2{x}^4+4c_1^3{x}^2+27x^4}+2c_1^3+27x^2}}{6\sqrt[3]{2}x}+\frac{(1-i\sqrt{3})(-3c_1{x}^2-c_1^2)}{32^{2/3}x\sqrt[3]{9c_1^2{x}^2+3\sqrt{3}\sqrt{-4c_1^3{x}^6-c_1^4{x}^4+18c_1^2{x}^4+4c_1^3{x}^2+27x^4}+2c_1^3+27x^2}}+\frac{c_1}{3x}\}\}$$

Maple: cpu = 0.156 (sec), leaf count = 583 $$\{y\left(x\right)=\frac{1}{12\mathit{\_}\mathit{C}\mathit{1}x}((-12i{x}^2\mathit{\_}\mathit{C}\mathit{1}-i{(108{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^2+18{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+(4x^4-4)\mathit{\_}\mathit{C}\mathit{1}-x^2}x\mathit{\_}\mathit{C}\mathit{1}+36x^2\mathit{\_}\mathit{C}\mathit{1}-8)}^{\frac{2}{3}}+4i)\sqrt{3}+12x^2\mathit{\_}\mathit{C}\mathit{1}-{(\sqrt[3]{108{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^2+18{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+(4x^4-4)\mathit{\_}\mathit{C}\mathit{1}-x^2}x\mathit{\_}\mathit{C}\mathit{1}+36x^2\mathit{\_}\mathit{C}\mathit{1}-8}+2)}^2)\frac{1}{\sqrt[3]{108{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^2+18{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+(4x^4-4)\mathit{\_}\mathit{C}\mathit{1}-x^2}x\mathit{\_}\mathit{C}\mathit{1}+36x^2\mathit{\_}\mathit{C}\mathit{1}-8}},y\left(x\right)=\frac{1}{12\mathit{\_}\mathit{C}\mathit{1}x}((12i{x}^2\mathit{\_}\mathit{C}\mathit{1}+i{(108{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^2+18{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+(4x^4-4)\mathit{\_}\mathit{C}\mathit{1}-x^2}x\mathit{\_}\mathit{C}\mathit{1}+36x^2\mathit{\_}\mathit{C}\mathit{1}-8)}^{\frac{2}{3}}-4i)\sqrt{3}+12x^2\mathit{\_}\mathit{C}\mathit{1}-{(\sqrt[3]{108{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^2+18{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+(4x^4-4)\mathit{\_}\mathit{C}\mathit{1}-x^2}x\mathit{\_}\mathit{C}\mathit{1}+36x^2\mathit{\_}\mathit{C}\mathit{1}-8}+2)}^2)\frac{1}{\sqrt[3]{108{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^2+18{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+(4x^4-4)\mathit{\_}\mathit{C}\mathit{1}-x^2}x\mathit{\_}\mathit{C}\mathit{1}+36x^2\mathit{\_}\mathit{C}\mathit{1}-8}},y\left(x\right)=\frac{1}{6\mathit{\_}\mathit{C}\mathit{1}x}\sqrt[3]{108{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^2+4\mathit{\_}\mathit{C}\mathit{1}{x}^4+18{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2-x^2-4\mathit{\_}\mathit{C}\mathit{1}}x\mathit{\_}\mathit{C}\mathit{1}+36x^2\mathit{\_}\mathit{C}\mathit{1}-8}-\frac{6x^2\mathit{\_}\mathit{C}\mathit{1}-2}{3\mathit{\_}\mathit{C}\mathit{1}x}\frac{1}{\sqrt[3]{108{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^2+4\mathit{\_}\mathit{C}\mathit{1}{x}^4+18{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2-x^2-4\mathit{\_}\mathit{C}\mathit{1}}x\mathit{\_}\mathit{C}\mathit{1}+36x^2\mathit{\_}\mathit{C}\mathit{1}-8}}-\frac{1}{3\mathit{\_}\mathit{C}\mathit{1}x}\}$$