3.752   ODE No. 752

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

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

Mathematica: cpu = 19.954034 (sec), leaf count = 39 $$\text{DSolve}[y^{\prime }(x)=\frac{\cos (y(x))(x^3\cos (y(x))-x-1)}{(x+1)(x\sin (y(x))-1)},y(x),x]$$

Maple: cpu = 1.060 (sec), leaf count = 874 $$\{y\left(x\right)=\arctan (-\frac{-2x^3+3x^2+6\ln (1+x)-6\mathit{\_}\mathit{C}\mathit{1}-6x}{4x^6-12x^5+24\mathit{\_}\mathit{C}\mathit{1}{x}^3+33x^4-24\ln (1+x)x^3-36x^2\mathit{\_}\mathit{C}\mathit{1}-36x^3+36\ln (1+x)x^2+36{\mathit{\_}\mathit{C}\mathit{1}}^2+72\mathit{\_}\mathit{C}\mathit{1}x-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)+36x^2-72\ln (1+x)x+36{(\ln (1+x))}^2+36}(-2x^4+3x^3+6\ln (1+x)x-6\mathit{\_}\mathit{C}\mathit{1}x-6x^2+\sqrt{4x^6-12x^5-24\ln (1+x)x^3+24\mathit{\_}\mathit{C}\mathit{1}{x}^3+33x^4+36\ln (1+x)x^2-36x^2\mathit{\_}\mathit{C}\mathit{1}-36x^3+36{(\ln (1+x))}^2-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)-72\ln (1+x)x+36{\mathit{\_}\mathit{C}\mathit{1}}^2+72\mathit{\_}\mathit{C}\mathit{1}x+36})+x,-6\frac{-2x^4+3x^3+6\ln (1+x)x-6\mathit{\_}\mathit{C}\mathit{1}x-6x^2+\sqrt{4x^6-12x^5-24\ln (1+x)x^3+24\mathit{\_}\mathit{C}\mathit{1}{x}^3+33x^4+36\ln (1+x)x^2-36x^2\mathit{\_}\mathit{C}\mathit{1}-36x^3+36{(\ln (1+x))}^2-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)-72\ln (1+x)x+36{\mathit{\_}\mathit{C}\mathit{1}}^2+72\mathit{\_}\mathit{C}\mathit{1}x+36}}{4x^6-12x^5+24\mathit{\_}\mathit{C}\mathit{1}{x}^3+33x^4-24\ln (1+x)x^3-36x^2\mathit{\_}\mathit{C}\mathit{1}-36x^3+36\ln (1+x)x^2+36{\mathit{\_}\mathit{C}\mathit{1}}^2+72\mathit{\_}\mathit{C}\mathit{1}x-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)+36x^2-72\ln (1+x)x+36{(\ln (1+x))}^2+36}),y\left(x\right)=\arctan (\frac{-2x^3+3x^2+6\ln (1+x)-6\mathit{\_}\mathit{C}\mathit{1}-6x}{4x^6-12x^5+24\mathit{\_}\mathit{C}\mathit{1}{x}^3+33x^4-24\ln (1+x)x^3-36x^2\mathit{\_}\mathit{C}\mathit{1}-36x^3+36\ln (1+x)x^2+36{\mathit{\_}\mathit{C}\mathit{1}}^2+72\mathit{\_}\mathit{C}\mathit{1}x-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)+36x^2-72\ln (1+x)x+36{(\ln (1+x))}^2+36}(2x^4-3x^3-6\ln (1+x)x+6\mathit{\_}\mathit{C}\mathit{1}x+6x^2+\sqrt{4x^6-12x^5-24\ln (1+x)x^3+24\mathit{\_}\mathit{C}\mathit{1}{x}^3+33x^4+36\ln (1+x)x^2-36x^2\mathit{\_}\mathit{C}\mathit{1}-36x^3+36{(\ln (1+x))}^2-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)-72\ln (1+x)x+36{\mathit{\_}\mathit{C}\mathit{1}}^2+72\mathit{\_}\mathit{C}\mathit{1}x+36})+x,6\frac{2x^4-3x^3-6\ln (1+x)x+6\mathit{\_}\mathit{C}\mathit{1}x+6x^2+\sqrt{4x^6-12x^5-24\ln (1+x)x^3+24\mathit{\_}\mathit{C}\mathit{1}{x}^3+33x^4+36\ln (1+x)x^2-36x^2\mathit{\_}\mathit{C}\mathit{1}-36x^3+36{(\ln (1+x))}^2-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)-72\ln (1+x)x+36{\mathit{\_}\mathit{C}\mathit{1}}^2+72\mathit{\_}\mathit{C}\mathit{1}x+36}}{4x^6-12x^5+24\mathit{\_}\mathit{C}\mathit{1}{x}^3+33x^4-24\ln (1+x)x^3-36x^2\mathit{\_}\mathit{C}\mathit{1}-36x^3+36\ln (1+x)x^2+36{\mathit{\_}\mathit{C}\mathit{1}}^2+72\mathit{\_}\mathit{C}\mathit{1}x-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)+36x^2-72\ln (1+x)x+36{(\ln (1+x))}^2+36})\}$$