11.22   ODE No. 1934

$$\boxed{{\displaystyle \{\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)=1/2{\left(x\left(t\right)\right)}^2-1/24y\left(t\right),\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)=2x\left(t\right)y\left(t\right)-3z\left(t\right),\frac{\mathrm{d}}{\mathrm{d}t}z\left(t\right)=3x\left(t\right)z\left(t\right)-1/6{\left(y\left(t\right)\right)}^2\}}}$$

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

Mathematica: cpu = 72.632223 (sec), leaf count = 66 $$\text{DSolve}[\{x^{\prime }(t)=\frac{x(t{)}^2}{2}-\frac{y(t)}{24},y^{\prime }(t)=2x(t)y(t)-3z(t),z^{\prime }(t)=3x(t)z(t)-\frac{y(t{)}^2}{6}\},\{x(t),y(t),z(t)\},t]$$

Maple: cpu = 0.904 (sec), leaf count = 376 $$\{[\{y\left(t\right)=0\},\{x\left(t\right)=2{(2\mathit{\_}\mathit{C}\mathit{1}-t)}^{-1}\},\{z\left(t\right)=0\}],[\{y\left(t\right)=256{(\mathit{\_}\mathit{C}\mathit{1}t+\mathit{\_}\mathit{C}\mathit{2})}^{-4}\},\{x\left(t\right)=\frac{1}{2y\left(t\right)}(\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)-\frac{\sqrt{3}}{3}{\left(y\left(t\right)\right)}^{\frac{3}{2}}),x\left(t\right)=\frac{1}{2y\left(t\right)}(\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)+\frac{\sqrt{3}}{3}{\left(y\left(t\right)\right)}^{\frac{3}{2}})\},\{z\left(t\right)=\frac{2x\left(t\right)y\left(t\right)}{3}-\frac{\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)}{3}\}],[\{y\left(t\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}({\mathrm{e}}^{\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{f}}\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)=-\frac{\sqrt{15}{\left(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)}^3}{20{\mathit{\_}\mathit{f}}^2}\sqrt{-\frac{{\mathit{\_}\mathit{f}}^2(3{\mathit{\_}\mathit{f}}^2\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)+12\mathit{\_}\mathit{f}-5\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)){(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathit{\_}\mathit{f}+4)}^2}{{\left(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)}^3}}+\frac{{\left(\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\right)}^2}{2}+\frac{\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)}{\mathit{\_}\mathit{f}}\},\{\mathit{\_}\mathit{f}=\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right){\left(y\left(t\right)\right)}^{-\frac{3}{2}},\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)=-2{\left(y\left(t\right)\right)}^{3/2}{(-2\frac{\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}y\left(t\right)\right)y\left(t\right)}{\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)}+3\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right))}^{-1}\},\{t=\int \frac{\mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)}{\mathit{\_}\mathit{f}}\frac{1}{\sqrt{{\mathrm{e}}^{\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2}}}}\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1},y\left(t\right)={\mathrm{e}}^{\int \mathit{\_}\mathit{g}\left(\mathit{\_}\mathit{f}\right)\mathrm{d}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2}}\}])\},\{x\left(t\right)=\frac{-2\left(\frac{{\mathrm{d}}^3}{\mathrm{d}{t}^3}y\left(t\right)\right)y\left(t\right)+3\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}y\left(t\right)\right)\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)}{-12\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}y\left(t\right)\right)y\left(t\right)+15{\left(\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)\right)}^2}\},\{z\left(t\right)=\frac{-4\left(\frac{{\mathrm{d}}^3}{\mathrm{d}{t}^3}y\left(t\right)\right){\left(y\left(t\right)\right)}^2+18\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}y\left(t\right)\right)y\left(t\right)\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)-15{\left(\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)\right)}^3}{-36\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}y\left(t\right)\right)y\left(t\right)+45{\left(\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)\right)}^2}\}]\}$$