3.821   ODE No. 821

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{y\left(x\right)(xy\left(x\right)+1)}{x(-xy\left(x\right)-1+{\left(y\left(x\right)\right)}^4{x}^3)}=0}}$$

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

Mathematica: cpu = 0.034004 (sec), leaf count = 2093 $$\{\{y(x)\to \frac{c_1}{4}-\frac{1}{2}\sqrt{\frac{c_1^2}{4}+\frac{\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}{18\sqrt[3]{2}{x}^3}+\frac{\sqrt[3]{2}(3c_1{x}^4+8x^3)}{x^3\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}}-\frac{1}{2}\sqrt{\frac{c_1^2}{2}-\frac{\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}{18\sqrt[3]{2}{x}^3}-\frac{\sqrt[3]{2}(3c_1{x}^4+8x^3)}{x^3\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}-\frac{c_1^3-\frac{4}{x^2}}{4\sqrt{\frac{c_1^2}{4}+\frac{\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}{18\sqrt[3]{2}{x}^3}+\frac{\sqrt[3]{2}(3c_1{x}^4+8x^3)}{x^3\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}}}}\},\{y(x)\to \frac{c_1}{4}-\frac{1}{2}\sqrt{\frac{c_1^2}{4}+\frac{\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}{18\sqrt[3]{2}{x}^3}+\frac{\sqrt[3]{2}(3c_1{x}^4+8x^3)}{x^3\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}}+\frac{1}{2}\sqrt{\frac{c_1^2}{2}-\frac{\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}{18\sqrt[3]{2}{x}^3}-\frac{\sqrt[3]{2}(3c_1{x}^4+8x^3)}{x^3\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}-\frac{c_1^3-\frac{4}{x^2}}{4\sqrt{\frac{c_1^2}{4}+\frac{\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}{18\sqrt[3]{2}{x}^3}+\frac{\sqrt[3]{2}(3c_1{x}^4+8x^3)}{x^3\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}}}}\},\{y(x)\to \frac{c_1}{4}+\frac{1}{2}\sqrt{\frac{c_1^2}{4}+\frac{\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}{18\sqrt[3]{2}{x}^3}+\frac{\sqrt[3]{2}(3c_1{x}^4+8x^3)}{x^3\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}}-\frac{1}{2}\sqrt{\frac{c_1^2}{2}-\frac{\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}{18\sqrt[3]{2}{x}^3}-\frac{\sqrt[3]{2}(3c_1{x}^4+8x^3)}{x^3\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}+\frac{c_1^3-\frac{4}{x^2}}{4\sqrt{\frac{c_1^2}{4}+\frac{\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}{18\sqrt[3]{2}{x}^3}+\frac{\sqrt[3]{2}(3c_1{x}^4+8x^3)}{x^3\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}}}}\},\{y(x)\to \frac{c_1}{4}+\frac{1}{2}\sqrt{\frac{c_1^2}{4}+\frac{\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}{18\sqrt[3]{2}{x}^3}+\frac{\sqrt[3]{2}(3c_1{x}^4+8x^3)}{x^3\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}}+\frac{1}{2}\sqrt{\frac{c_1^2}{2}-\frac{\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}{18\sqrt[3]{2}{x}^3}-\frac{\sqrt[3]{2}(3c_1{x}^4+8x^3)}{x^3\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}+\frac{c_1^3-\frac{4}{x^2}}{4\sqrt{\frac{c_1^2}{4}+\frac{\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}{18\sqrt[3]{2}{x}^3}+\frac{\sqrt[3]{2}(3c_1{x}^4+8x^3)}{x^3\sqrt[3]{1944c_1^2{x}^6+1458x^5+\sqrt{(1944c_1^2{x}^6+1458x^5){}^2-4(54c_1{x}^4+144x^3){}^3}}}}}}\}\}$$

Maple: cpu = 0.124 (sec), leaf count = 27 $$\{-\frac{1}{2x^2{\left(y\left(x\right)\right)}^2}-\frac{1}{3x^3{\left(y\left(x\right)\right)}^3}-y\left(x\right)+\mathit{\_}\mathit{C}\mathit{1}=0\}$$