11.5   ODE No. 1917

$$\boxed{{\displaystyle \{\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)={\left(y\left(t\right)\right)}^2-\cos \left(x\left(t\right)\right),\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)=-y\left(t\right)\sin \left(x\left(t\right)\right)\}}}$$

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

Mathematica: cpu = 250.096758 (sec), leaf count = 35 $$\text{DSolve}[\{x^{\prime }(t)=y(t{)}^2-\cos (x(t)),y^{\prime }(t)=y(t)(-\sin (x(t)))\},\{x(t),y(t)\},t]$$

Maple: cpu = 0.593 (sec), leaf count = 109 $$\{[\{x\left(t\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(2{\int }^{\mathit{\_}\mathit{Z}}{(\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-3\sqrt{-{(\cos \left(\mathit{\_}\mathit{f}\right))}^2}\ln \left(9/4\frac{{(\cos \left(\mathit{\_}\mathit{f}\right))}^2}{{(\cos \left(\mathit{\_}\mathit{Z}\right))}^2}\right)+3\mathit{\_}\mathit{C}\mathit{1}\sqrt{-{(\cos \left(\mathit{\_}\mathit{f}\right))}^2}+2\mathit{\_}\mathit{Z}\cos \left(\mathit{\_}\mathit{f}\right))\right)\sqrt{-4\cos \left(2\mathit{\_}\mathit{f}\right)-4-{(\cos \left(\mathit{\_}\mathit{f}\right))}^2}-\cos \left(\mathit{\_}\mathit{f}\right))}^{-1}d\mathit{\_}\mathit{f}+t+\mathit{\_}\mathit{C}\mathit{2})\},\{y\left(t\right)=\sqrt{\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+\cos \left(x\left(t\right)\right)},y\left(t\right)=-\sqrt{\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+\cos \left(x\left(t\right)\right)}\}]\}$$