2.832   ODE No. 832

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

$$y^{\prime }(x)=\frac{y(x)(y(x)+x+1)}{(x+1)(y(x{)}^4+y(x{)}^3+y(x{)}^2+x)}$$ ✓ Mathematica : cpu = 3.3505 (sec), leaf count = 2497

$$\{\{y(x)\to -\frac{1}{2}\sqrt{\frac{3\sqrt[3]{2}(-8x+3c_1+3\log (x+1)+2)}{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}+\frac{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}{6\sqrt[3]{2}}-\frac{23}{16}}-\frac{1}{2}\sqrt{-\frac{3\sqrt[3]{2}(-8x+3c_1+3\log (x+1)+2)}{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}-\frac{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}{6\sqrt[3]{2}}-\frac{24(c_1+\log (x+1))[phone]\frac{\mathrm{}}{\mathrm{}}}{\mathrm{}\sqrt{\frac{\mathrm{}\sqrt[\mathrm{}]{\mathrm{}}(-8x+3c_1+3\log (x+1)+2)}{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}+\frac{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}{6\sqrt[3]{2}}-\frac{23}{16}}}-\frac{23}{8}}-\frac{3}{8}\},\{y(x)\to -\frac{1}{2}\sqrt{\frac{3\sqrt[3]{2}(-8x+3c_1+3\log (x+1)+2)}{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}+\frac{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}{6\sqrt[3]{2}}-\frac{23}{16}}+\frac{1}{2}\sqrt{-\frac{3\sqrt[3]{2}(-8x+3c_1+3\log (x+1)+2)}{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}-\frac{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}{6\sqrt[3]{2}}-\frac{24(c_1+\log (x+1))[phone]\frac{\mathrm{}}{\mathrm{}}}{\mathrm{}\sqrt{\frac{\mathrm{}\sqrt[\mathrm{}]{\mathrm{}}(-8x+3c_1+3\log (x+1)+2)}{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}+\frac{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}{6\sqrt[3]{2}}-\frac{23}{16}}}-\frac{23}{8}}-\frac{3}{8}\},\{y(x)\to \frac{1}{2}\sqrt{\frac{3\sqrt[3]{2}(-8x+3c_1+3\log (x+1)+2)}{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}+\frac{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}{6\sqrt[3]{2}}-\frac{23}{16}}-\frac{1}{2}\sqrt{-\frac{3\sqrt[3]{2}(-8x+3c_1+3\log (x+1)+2)}{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}-\frac{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}{6\sqrt[3]{2}}+\frac{24(c_1+\log (x+1))[phone]\frac{\mathrm{}}{\mathrm{}}}{\mathrm{}\sqrt{\frac{\mathrm{}\sqrt[\mathrm{}]{\mathrm{}}(-8x+3c_1+3\log (x+1)+2)}{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}+\frac{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}{6\sqrt[3]{2}}-\frac{23}{16}}}-\frac{23}{8}}-\frac{3}{8}\},\{y(x)\to \frac{1}{2}\sqrt{\frac{3\sqrt[3]{2}(-8x+3c_1+3\log (x+1)+2)}{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}+\frac{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}{6\sqrt[3]{2}}-\frac{23}{16}}+\frac{1}{2}\sqrt{-\frac{3\sqrt[3]{2}(-8x+3c_1+3\log (x+1)+2)}{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}-\frac{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}{6\sqrt[3]{2}}+\frac{24(c_1+\log (x+1))[phone]\frac{\mathrm{}}{\mathrm{}}}{\mathrm{}\sqrt{\frac{\mathrm{}\sqrt[\mathrm{}]{\mathrm{}}(-8x+3c_1+3\log (x+1)+2)}{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}+\frac{\sqrt[3]{1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+\sqrt{(1944(c_1+\log (x+1)){}^2+972(c_1+\log (x+1))+3726x+432){}^2-4(-144x+54(c_1+\log (x+1))+36){}^3}+432}}{6\sqrt[3]{2}}-\frac{23}{16}}}-\frac{23}{8}}-\frac{3}{8}\}\}$$

✓ Maple : cpu = 0.194 (sec), leaf count = 31

$$\{\ln (1+x)+\frac{x}{y\left(x\right)}-\frac{{\left(y\left(x\right)\right)}^3}{3}-\frac{{\left(y\left(x\right)\right)}^2}{2}-y\left(x\right)+\mathit{\_}\mathit{C}\mathit{1}=0\}$$