2.983   ODE No. 983

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

$$y^{\prime }(x)=\frac{-x^3+3x^{2}y(x)+x^2-3xy(x{)}^2+y(x{)}^3}{(x-1)(x+1)}$$ ✓ Mathematica : cpu = 0.254323 (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 = 0.278 (sec), leaf count = 469

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