3.983   ODE No. 983

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{{\left(y\left(x\right)\right)}^3-3x{\left(y\left(x\right)\right)}^2+3x^{2}y\left(x\right)-x^3+x^2}{(1+x)(x-1)}=0}}$$

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

Mathematica: cpu = 0.255032 (sec), leaf count = 238 $$\text{Solve}[\frac{1}{3}\log (\frac{\frac{3y(x)}{x^2-1}-\frac{3x}{x^2-1}}{3\sqrt[3]{\frac{1}{(x-1{)}^3(x+1{)}^3}}}+1)-\frac{1}{6}\log (\frac{{(\frac{3y(x)}{x^2-1}-\frac{3x}{x^2-1})}^2}{9{\left(\frac{1}{(x-1{)}^3(x+1{)}^3}\right)}^{2/3}}-\frac{\frac{3y(x)}{x^2-1}-\frac{3x}{x^2-1}}{3\sqrt[3]{\frac{1}{(x-1{)}^3(x+1{)}^3}}}+1)+\frac{{\tan }^{-1}\left(\frac{\frac{2(\frac{3y(x)}{x^2-1}-\frac{3x}{x^2-1})}{3\sqrt[3]{\frac{1}{(x-1{)}^3(x+1{)}^3}}}-1}{\sqrt{3}}\right)}{\sqrt{3}}=c_1+\frac{1}{2}{\left(\frac{1}{{(x^2-1)}^3}\right)}^{2/3}{(x^2-1)}^2(\log (1-x)-\log (x+1)),y(x)]$$

Maple: cpu = 0.203 (sec), leaf count = 469 $$\{y\left(x\right)=\frac{\sqrt{3}}{6}(\sqrt[3]{\frac{1}{{(1+x)}^3{(x-1)}^3}}\sqrt{3}{x}^2+3\sqrt[3]{\frac{1}{{(1+x)}^3{(x-1)}^3}}\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-18\ln (1+x){\left(\frac{1}{{(1+x)}^3{(x-1)}^3}\right)}^{2/3}{x}^4+18{\left(\frac{1}{{(1+x)}^3{(x-1)}^3}\right)}^{2/3}\ln (x-1)x^4+36\ln (1+x){\left(\frac{1}{{(1+x)}^3{(x-1)}^3}\right)}^{2/3}{x}^2-36{\left(\frac{1}{{(1+x)}^3{(x-1)}^3}\right)}^{2/3}\ln (x-1)x^2-18\ln (1+x){\left(\frac{1}{{(1+x)}^3{(x-1)}^3}\right)}^{2/3}+18\ln (x-1){\left(\frac{1}{{(1+x)}^3{(x-1)}^3}\right)}^{2/3}-12\mathit{\_}\mathit{Z}\sqrt{3}-4\ln \left(3/8\frac{{(\sqrt{3}+\tan \left(\mathit{\_}\mathit{Z}\right))}^3\sqrt{3}}{{(1+x)}^3{(x-1)}^3}\right)+4\ln \left(\frac{1}{{(1+x)}^3{(x-1)}^3}\right)-6\ln \left(4/3{({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+1)}^{-1}\right)+36\mathit{\_}\mathit{C}\mathit{1})\right)x^2-\sqrt[3]{\frac{1}{{(1+x)}^3{(x-1)}^3}}\sqrt{3}-3\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-18\ln (1+x){\left(\frac{1}{{(1+x)}^3{(x-1)}^3}\right)}^{2/3}{x}^4+18{\left(\frac{1}{{(1+x)}^3{(x-1)}^3}\right)}^{2/3}\ln (x-1)x^4+36\ln (1+x){\left(\frac{1}{{(1+x)}^3{(x-1)}^3}\right)}^{2/3}{x}^2-36{\left(\frac{1}{{(1+x)}^3{(x-1)}^3}\right)}^{2/3}\ln (x-1)x^2-18\ln (1+x){\left(\frac{1}{{(1+x)}^3{(x-1)}^3}\right)}^{2/3}+18\ln (x-1){\left(\frac{1}{{(1+x)}^3{(x-1)}^3}\right)}^{2/3}-12\mathit{\_}\mathit{Z}\sqrt{3}-4\ln \left(3/8\frac{{(\sqrt{3}+\tan \left(\mathit{\_}\mathit{Z}\right))}^3\sqrt{3}}{{(1+x)}^3{(x-1)}^3}\right)+4\ln \left(\frac{1}{{(1+x)}^3{(x-1)}^3}\right)-6\ln \left(4/3{({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+1)}^{-1}\right)+36\mathit{\_}\mathit{C}\mathit{1})\right)\sqrt[3]{\frac{1}{{(1+x)}^3{(x-1)}^3}}+2\sqrt{3}x)\}$$