3.770   ODE No. 770

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=2\frac{{\left(y\left(x\right)\right)}^6}{{\left(y\left(x\right)\right)}^3+2+16x{\left(y\left(x\right)\right)}^2+32x^2{\left(y\left(x\right)\right)}^4}=0}}$$

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

Mathematica: cpu = 0.105513 (sec), leaf count = 705 $$\{\{y(x)\to \frac{\sqrt[3]{18432c_1^2{x}^2+\sqrt{4(192c_1^{2}x-12c_1-256x^2){}^3+(18432c_1^2{x}^2-2880c_{1}x+8192x^3+108){}^2}-2880c_{1}x+8192x^3+108}}{3\sqrt[3]{2}(1-16c_{1}x)}-\frac{\sqrt[3]{2}(192c_1^{2}x-12c_1-256x^2)}{3(1-16c_{1}x)\sqrt[3]{18432c_1^2{x}^2+\sqrt{4(192c_1^{2}x-12c_1-256x^2){}^3+(18432c_1^2{x}^2-2880c_{1}x+8192x^3+108){}^2}-2880c_{1}x+8192x^3+108}}+\frac{16x}{3(1-16c_{1}x)}\},\{y(x)\to -\frac{(1-i\sqrt{3})\sqrt[3]{18432c_1^2{x}^2+\sqrt{4(192c_1^{2}x-12c_1-256x^2){}^3+(18432c_1^2{x}^2-2880c_{1}x+8192x^3+108){}^2}-2880c_{1}x+8192x^3+108}}{6\sqrt[3]{2}(1-16c_{1}x)}+\frac{(1+i\sqrt{3})(192c_1^{2}x-12c_1-256x^2)}{32^{2/3}(1-16c_{1}x)\sqrt[3]{18432c_1^2{x}^2+\sqrt{4(192c_1^{2}x-12c_1-256x^2){}^3+(18432c_1^2{x}^2-2880c_{1}x+8192x^3+108){}^2}-2880c_{1}x+8192x^3+108}}+\frac{16x}{3(1-16c_{1}x)}\},\{y(x)\to -\frac{(1+i\sqrt{3})\sqrt[3]{18432c_1^2{x}^2+\sqrt{4(192c_1^{2}x-12c_1-256x^2){}^3+(18432c_1^2{x}^2-2880c_{1}x+8192x^3+108){}^2}-2880c_{1}x+8192x^3+108}}{6\sqrt[3]{2}(1-16c_{1}x)}+\frac{(1-i\sqrt{3})(192c_1^{2}x-12c_1-256x^2)}{32^{2/3}(1-16c_{1}x)\sqrt[3]{18432c_1^2{x}^2+\sqrt{4(192c_1^{2}x-12c_1-256x^2){}^3+(18432c_1^2{x}^2-2880c_{1}x+8192x^3+108){}^2}-2880c_{1}x+8192x^3+108}}+\frac{16x}{3(1-16c_{1}x)}\}\}$$

Maple: cpu = 0.094 (sec), leaf count = 1345 $$\{y\left(x\right)=\frac{1}{3\mathit{\_}\mathit{C}\mathit{1}+48x}\sqrt[3]{4096{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^3+6\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}\mathit{\_}\mathit{C}\mathit{1}+96\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}x+54{\mathit{\_}\mathit{C}\mathit{1}}^3+1440{\mathit{\_}\mathit{C}\mathit{1}}^{2}x+9216x^2\mathit{\_}\mathit{C}\mathit{1}}+\frac{256{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2-12\mathit{\_}\mathit{C}\mathit{1}-192x}{3\mathit{\_}\mathit{C}\mathit{1}+48x}\frac{1}{\sqrt[3]{4096{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^3+6\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}\mathit{\_}\mathit{C}\mathit{1}+96\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}x+54{\mathit{\_}\mathit{C}\mathit{1}}^3+1440{\mathit{\_}\mathit{C}\mathit{1}}^{2}x+9216x^2\mathit{\_}\mathit{C}\mathit{1}}}+\frac{16\mathit{\_}\mathit{C}\mathit{1}x}{3\mathit{\_}\mathit{C}\mathit{1}+48x},y\left(x\right)=-\frac{1}{6\mathit{\_}\mathit{C}\mathit{1}+96x}\sqrt[3]{4096{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^3+6\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}\mathit{\_}\mathit{C}\mathit{1}+96\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}x+54{\mathit{\_}\mathit{C}\mathit{1}}^3+1440{\mathit{\_}\mathit{C}\mathit{1}}^{2}x+9216x^2\mathit{\_}\mathit{C}\mathit{1}}-\frac{128{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2-6\mathit{\_}\mathit{C}\mathit{1}-96x}{3\mathit{\_}\mathit{C}\mathit{1}+48x}\frac{1}{\sqrt[3]{4096{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^3+6\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}\mathit{\_}\mathit{C}\mathit{1}+96\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}x+54{\mathit{\_}\mathit{C}\mathit{1}}^3+1440{\mathit{\_}\mathit{C}\mathit{1}}^{2}x+9216x^2\mathit{\_}\mathit{C}\mathit{1}}}+\frac{16\mathit{\_}\mathit{C}\mathit{1}x}{3\mathit{\_}\mathit{C}\mathit{1}+48x}-\frac{i}{2}\sqrt{3}(\frac{1}{3\mathit{\_}\mathit{C}\mathit{1}+48x}\sqrt[3]{4096{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^3+6\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}\mathit{\_}\mathit{C}\mathit{1}+96\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}x+54{\mathit{\_}\mathit{C}\mathit{1}}^3+1440{\mathit{\_}\mathit{C}\mathit{1}}^{2}x+9216x^2\mathit{\_}\mathit{C}\mathit{1}}-\frac{256{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2-12\mathit{\_}\mathit{C}\mathit{1}-192x}{3\mathit{\_}\mathit{C}\mathit{1}+48x}\frac{1}{\sqrt[3]{4096{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^3+6\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}\mathit{\_}\mathit{C}\mathit{1}+96\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}x+54{\mathit{\_}\mathit{C}\mathit{1}}^3+1440{\mathit{\_}\mathit{C}\mathit{1}}^{2}x+9216x^2\mathit{\_}\mathit{C}\mathit{1}}}),y\left(x\right)=-\frac{1}{6\mathit{\_}\mathit{C}\mathit{1}+96x}\sqrt[3]{4096{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^3+6\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}\mathit{\_}\mathit{C}\mathit{1}+96\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}x+54{\mathit{\_}\mathit{C}\mathit{1}}^3+1440{\mathit{\_}\mathit{C}\mathit{1}}^{2}x+9216x^2\mathit{\_}\mathit{C}\mathit{1}}-\frac{128{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2-6\mathit{\_}\mathit{C}\mathit{1}-96x}{3\mathit{\_}\mathit{C}\mathit{1}+48x}\frac{1}{\sqrt[3]{4096{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^3+6\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}\mathit{\_}\mathit{C}\mathit{1}+96\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}x+54{\mathit{\_}\mathit{C}\mathit{1}}^3+1440{\mathit{\_}\mathit{C}\mathit{1}}^{2}x+9216x^2\mathit{\_}\mathit{C}\mathit{1}}}+\frac{16\mathit{\_}\mathit{C}\mathit{1}x}{3\mathit{\_}\mathit{C}\mathit{1}+48x}+\frac{i}{2}\sqrt{3}(\frac{1}{3\mathit{\_}\mathit{C}\mathit{1}+48x}\sqrt[3]{4096{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^3+6\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}\mathit{\_}\mathit{C}\mathit{1}+96\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}x+54{\mathit{\_}\mathit{C}\mathit{1}}^3+1440{\mathit{\_}\mathit{C}\mathit{1}}^{2}x+9216x^2\mathit{\_}\mathit{C}\mathit{1}}-\frac{256{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2-12\mathit{\_}\mathit{C}\mathit{1}-192x}{3\mathit{\_}\mathit{C}\mathit{1}+48x}\frac{1}{\sqrt[3]{4096{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^3+6\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}\mathit{\_}\mathit{C}\mathit{1}+96\sqrt{3}\sqrt{4096{\mathit{\_}\mathit{C}\mathit{1}}^4{x}^3+27{\mathit{\_}\mathit{C}\mathit{1}}^4+576x{\mathit{\_}\mathit{C}\mathit{1}}^3+2048{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+16\mathit{\_}\mathit{C}\mathit{1}+256x}x+54{\mathit{\_}\mathit{C}\mathit{1}}^3+1440{\mathit{\_}\mathit{C}\mathit{1}}^{2}x+9216x^2\mathit{\_}\mathit{C}\mathit{1}}})\}$$