2.752   ODE No. 752

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

$$y^{\prime }(x)=\frac{\cos (y(x))(x^3\cos (y(x))-x-1)}{(x+1)(x\sin (y(x))-1)}$$ ✗ Mathematica : cpu = 31.4812 (sec), leaf count = 0 , could not solve

DSolve[Derivative[1][y][x] == (Cos[y[x]]*(-1 - x + x^3*Cos[y[x]]))/((1 + x)*(-1 + x*Sin[y[x]])), y[x], x]

✓ Maple : cpu = 1.672 (sec), leaf count = 879

$$\{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^4-24x^3\ln (1+x)-36\mathit{\_}\mathit{C}\mathit{1}{x}^2-36x^3+36x^2\ln (1+x)+36{\mathit{\_}\mathit{C}\mathit{1}}^2+72\mathit{\_}\mathit{C}\mathit{1}x-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)+36x^2-72x\ln (1+x)+36{(\ln (1+x))}^2+36}(-2x^4+3x^3+6x\ln (1+x)-6\mathit{\_}\mathit{C}\mathit{1}x-6x^2-\sqrt{4x^6-12x^5-24x^3\ln (1+x)+24\mathit{\_}\mathit{C}\mathit{1}{x}^3+33x^4+36x^2\ln (1+x)-36\mathit{\_}\mathit{C}\mathit{1}{x}^2-36x^3+36{(\ln (1+x))}^2-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)-72x\ln (1+x)+36{\mathit{\_}\mathit{C}\mathit{1}}^2+72\mathit{\_}\mathit{C}\mathit{1}x+36})+x,-6\frac{-2x^4+3x^3+6x\ln (1+x)-6\mathit{\_}\mathit{C}\mathit{1}x-6x^2-\sqrt{4x^6-12x^5-24x^3\ln (1+x)+24\mathit{\_}\mathit{C}\mathit{1}{x}^3+33x^4+36x^2\ln (1+x)-36\mathit{\_}\mathit{C}\mathit{1}{x}^2-36x^3+36{(\ln (1+x))}^2-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)-72x\ln (1+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^4-24x^3\ln (1+x)-36\mathit{\_}\mathit{C}\mathit{1}{x}^2-36x^3+36x^2\ln (1+x)+36{\mathit{\_}\mathit{C}\mathit{1}}^2+72\mathit{\_}\mathit{C}\mathit{1}x-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)+36x^2-72x\ln (1+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^4-24x^3\ln (1+x)-36\mathit{\_}\mathit{C}\mathit{1}{x}^2-36x^3+36x^2\ln (1+x)+36{\mathit{\_}\mathit{C}\mathit{1}}^2+72\mathit{\_}\mathit{C}\mathit{1}x-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)+36x^2-72x\ln (1+x)+36{(\ln (1+x))}^2+36}(-2x^4+3x^3+6x\ln (1+x)-6\mathit{\_}\mathit{C}\mathit{1}x-6x^2+\sqrt{4x^6-12x^5-24x^3\ln (1+x)+24\mathit{\_}\mathit{C}\mathit{1}{x}^3+33x^4+36x^2\ln (1+x)-36\mathit{\_}\mathit{C}\mathit{1}{x}^2-36x^3+36{(\ln (1+x))}^2-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)-72x\ln (1+x)+36{\mathit{\_}\mathit{C}\mathit{1}}^2+72\mathit{\_}\mathit{C}\mathit{1}x+36})+x,-6\frac{-2x^4+3x^3+6x\ln (1+x)-6\mathit{\_}\mathit{C}\mathit{1}x-6x^2+\sqrt{4x^6-12x^5-24x^3\ln (1+x)+24\mathit{\_}\mathit{C}\mathit{1}{x}^3+33x^4+36x^2\ln (1+x)-36\mathit{\_}\mathit{C}\mathit{1}{x}^2-36x^3+36{(\ln (1+x))}^2-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)-72x\ln (1+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^4-24x^3\ln (1+x)-36\mathit{\_}\mathit{C}\mathit{1}{x}^2-36x^3+36x^2\ln (1+x)+36{\mathit{\_}\mathit{C}\mathit{1}}^2+72\mathit{\_}\mathit{C}\mathit{1}x-72\mathit{\_}\mathit{C}\mathit{1}\ln (1+x)+36x^2-72x\ln (1+x)+36{(\ln (1+x))}^2+36})\}$$