2.770   ODE No. 770

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

$$y^{\prime }(x)=\frac{2y(x{)}^6}{32x^{2}y(x{)}^4+y(x{)}^3+16xy(x{)}^2+2}$$ ✓ Mathematica : cpu = 0.209494 (sec), leaf count = 705

$$\{\{y(x)\to \frac{\sqrt[3]{8192x^3+18432c_1{}^2{x}^2+\sqrt{4(-256x^2+192c_1{}^{2}x-12c_1){}^3+(8192x^3+18432c_1{}^2{x}^2-2880c_{1}x+108){}^2}-2880c_{1}x+108}}{3\sqrt[3]{2}(1-16c_{1}x)}-\frac{\sqrt[3]{2}(-256x^2+192c_1{}^{2}x-12c_1)}{3(1-16c_{1}x)\sqrt[3]{8192x^3+18432c_1{}^2{x}^2+\sqrt{4(-256x^2+192c_1{}^{2}x-12c_1){}^3+(8192x^3+18432c_1{}^2{x}^2-2880c_{1}x+108){}^2}-2880c_{1}x+108}}+\frac{16x}{3(1-16c_{1}x)}\},\{y(x)\to -\frac{(1-i\sqrt{3})\sqrt[3]{8192x^3+18432c_1{}^2{x}^2+\sqrt{4(-256x^2+192c_1{}^{2}x-12c_1){}^3+(8192x^3+18432c_1{}^2{x}^2-2880c_{1}x+108){}^2}-2880c_{1}x+108}}{6\sqrt[3]{2}(1-16c_{1}x)}+\frac{(1+i\sqrt{3})(-256x^2+192c_1{}^{2}x-12c_1)}{32^{2/3}(1-16c_{1}x)\sqrt[3]{8192x^3+18432c_1{}^2{x}^2+\sqrt{4(-256x^2+192c_1{}^{2}x-12c_1){}^3+(8192x^3+18432c_1{}^2{x}^2-2880c_{1}x+108){}^2}-2880c_{1}x+108}}+\frac{16x}{3(1-16c_{1}x)}\},\{y(x)\to -\frac{(1+i\sqrt{3})\sqrt[3]{8192x^3+18432c_1{}^2{x}^2+\sqrt{4(-256x^2+192c_1{}^{2}x-12c_1){}^3+(8192x^3+18432c_1{}^2{x}^2-2880c_{1}x+108){}^2}-2880c_{1}x+108}}{6\sqrt[3]{2}(1-16c_{1}x)}+\frac{(1-i\sqrt{3})(-256x^2+192c_1{}^{2}x-12c_1)}{32^{2/3}(1-16c_{1}x)\sqrt[3]{8192x^3+18432c_1{}^2{x}^2+\sqrt{4(-256x^2+192c_1{}^{2}x-12c_1){}^3+(8192x^3+18432c_1{}^2{x}^2-2880c_{1}x+108){}^2}-2880c_{1}x+108}}+\frac{16x}{3(1-16c_{1}x)}\}\}$$ ✓ Maple : cpu = 0.165 (sec), leaf count = 1105

$$\{y\left(x\right)=\frac{1}{96x+6\mathit{\_}\mathit{C}\mathit{1}}(32\mathit{\_}\mathit{C}\mathit{1}x\sqrt[3]{96\sqrt{3}(\mathit{\_}\mathit{C}\mathit{1}/16+x)\sqrt{(4096x^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}+(4096x^3+54){\mathit{\_}\mathit{C}\mathit{1}}^3+1440x{\mathit{\_}\mathit{C}\mathit{1}}^2+9216\mathit{\_}\mathit{C}\mathit{1}{x}^2}+(-256i{x}^2{\mathit{\_}\mathit{C}\mathit{1}}^2+i{(4096{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^3+6\sqrt{3}\sqrt{(4096x^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{(4096x^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+1440x{\mathit{\_}\mathit{C}\mathit{1}}^2+9216\mathit{\_}\mathit{C}\mathit{1}{x}^2)}^{\frac{2}{3}}+192ix+12i\mathit{\_}\mathit{C}\mathit{1})\sqrt{3}-256{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2-{(4096{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^3+6\sqrt{3}\sqrt{(4096x^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{(4096x^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+1440x{\mathit{\_}\mathit{C}\mathit{1}}^2+9216\mathit{\_}\mathit{C}\mathit{1}{x}^2)}^{\frac{2}{3}}+192x+12\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt[3]{96\sqrt{3}(\mathit{\_}\mathit{C}\mathit{1}/16+x)\sqrt{(4096x^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}+(4096x^3+54){\mathit{\_}\mathit{C}\mathit{1}}^3+1440x{\mathit{\_}\mathit{C}\mathit{1}}^2+9216\mathit{\_}\mathit{C}\mathit{1}{x}^2}},y\left(x\right)=-\frac{1}{96x+6\mathit{\_}\mathit{C}\mathit{1}}(-32\mathit{\_}\mathit{C}\mathit{1}x\sqrt[3]{96\sqrt{3}(\mathit{\_}\mathit{C}\mathit{1}/16+x)\sqrt{(4096x^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}+(4096x^3+54){\mathit{\_}\mathit{C}\mathit{1}}^3+1440x{\mathit{\_}\mathit{C}\mathit{1}}^2+9216\mathit{\_}\mathit{C}\mathit{1}{x}^2}+(-256i{x}^2{\mathit{\_}\mathit{C}\mathit{1}}^2+i{(4096{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^3+6\sqrt{3}\sqrt{(4096x^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{(4096x^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+1440x{\mathit{\_}\mathit{C}\mathit{1}}^2+9216\mathit{\_}\mathit{C}\mathit{1}{x}^2)}^{\frac{2}{3}}+192ix+12i\mathit{\_}\mathit{C}\mathit{1})\sqrt{3}+256{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+{(4096{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^3+6\sqrt{3}\sqrt{(4096x^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{(4096x^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+1440x{\mathit{\_}\mathit{C}\mathit{1}}^2+9216\mathit{\_}\mathit{C}\mathit{1}{x}^2)}^{\frac{2}{3}}-192x-12\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt[3]{96\sqrt{3}(\mathit{\_}\mathit{C}\mathit{1}/16+x)\sqrt{(4096x^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}+(4096x^3+54){\mathit{\_}\mathit{C}\mathit{1}}^3+1440x{\mathit{\_}\mathit{C}\mathit{1}}^2+9216\mathit{\_}\mathit{C}\mathit{1}{x}^2}},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+1440x{\mathit{\_}\mathit{C}\mathit{1}}^2+9216\mathit{\_}\mathit{C}\mathit{1}{x}^2}+\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+1440x{\mathit{\_}\mathit{C}\mathit{1}}^2+9216\mathit{\_}\mathit{C}\mathit{1}{x}^2}}+16\frac{\mathit{\_}\mathit{C}\mathit{1}x}{3\mathit{\_}\mathit{C}\mathit{1}+48x}\}$$