2.742   ODE No. 742

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

$$y^{\prime }(x)=-\frac{(-\cos (y(x))+x+1)\cos (y(x))}{(x+1)(x\sin (y(x))-1)}$$ ✓ Mathematica : cpu = 3.07936 (sec), leaf count = 3913

$$\{\{y(x)\to -{\sec }^{-1}(\frac{c_1{x}^3}{x^2-1}+\frac{\log (x+1)x^3}{x^2-1}-\frac{c_1{}^3{x}^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{{\log }^3(x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{3c_1{\log }^2(x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{c_1{x}^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{3c_1{}^2\log (x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{\log (x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{c_1{}^2\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{{\log }^2(x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{2c_1\log (x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}+\frac{c_{1}x}{x^2-1}-c_{1}x+\frac{\log (x+1)x}{x^2-1}-\log (x+1)x+\frac{c_1{}^{3}x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{{\log }^3(x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{3c_1{\log }^2(x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{c_{1}x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{3c_1{}^2\log (x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{\log (x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{c_1{}^2\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{{\log }^2(x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{2c_1\log (x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1})\},\{y(x)\to {\sec }^{-1}(\frac{c_1{x}^3}{x^2-1}+\frac{\log (x+1)x^3}{x^2-1}-\frac{c_1{}^3{x}^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{{\log }^3(x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{3c_1{\log }^2(x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{c_1{x}^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{3c_1{}^2\log (x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{\log (x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{c_1{}^2\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{{\log }^2(x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{2c_1\log (x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}+\frac{c_{1}x}{x^2-1}-c_{1}x+\frac{\log (x+1)x}{x^2-1}-\log (x+1)x+\frac{c_1{}^{3}x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{{\log }^3(x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{3c_1{\log }^2(x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{c_{1}x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{3c_1{}^2\log (x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{\log (x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{c_1{}^2\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{{\log }^2(x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{2c_1\log (x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1})\},\{y(x)\to -{\sec }^{-1}(\frac{c_1{x}^3}{x^2-1}+\frac{\log (x+1)x^3}{x^2-1}-\frac{c_1{}^3{x}^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{{\log }^3(x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{3c_1{\log }^2(x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{c_1{x}^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{3c_1{}^2\log (x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{\log (x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}+\frac{c_1{}^2\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}+\frac{{\log }^2(x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}+\frac{2c_1\log (x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}+\frac{\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}+\frac{c_{1}x}{x^2-1}-c_{1}x+\frac{\log (x+1)x}{x^2-1}-\log (x+1)x+\frac{c_1{}^{3}x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{{\log }^3(x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{3c_1{\log }^2(x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{c_{1}x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{3c_1{}^2\log (x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{\log (x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}-\frac{c_1{}^2\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}-\frac{{\log }^2(x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}-\frac{2c_1\log (x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}-\frac{\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1})\},\{y(x)\to {\sec }^{-1}(\frac{c_1{x}^3}{x^2-1}+\frac{\log (x+1)x^3}{x^2-1}-\frac{c_1{}^3{x}^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{{\log }^3(x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{3c_1{\log }^2(x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{c_1{x}^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{3c_1{}^2\log (x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}-\frac{\log (x+1)x^3}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}+\frac{c_1{}^2\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}+\frac{{\log }^2(x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}+\frac{2c_1\log (x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}+\frac{\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}{x}^2}{(x^2-1)(c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1)}+\frac{c_{1}x}{x^2-1}-c_{1}x+\frac{\log (x+1)x}{x^2-1}-\log (x+1)x+\frac{c_1{}^{3}x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{{\log }^3(x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{3c_1{\log }^2(x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{c_{1}x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{3c_1{}^2\log (x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}+\frac{\log (x+1)x}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}-\frac{c_1{}^2\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}-\frac{{\log }^2(x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}-\frac{2c_1\log (x+1)\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1}-\frac{\sqrt{-x^2+c_1{}^2+{\log }^2(x+1)+2c_1\log (x+1)+1}}{c_1{}^2+2\log (x+1)c_1+{\log }^2(x+1)+1})\}\}$$ ✓ Maple : cpu = 1.654 (sec), leaf count = 239

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