11.18   ODE No. 1930

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

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

Mathematica: cpu = 0.052507 (sec), leaf count = 308 $$\left\{\{x(t)\to e^{-c_3}(e^{c_3}{c}_1+e^t),y(t)\to c_2(e^{-c_3}(e^{c_3}{c}_1+e^t)-c_1)+(e^{-c_3}(e^{c_3}{c}_1+e^t)-c_1)(-\frac{c_1^2}{e^{-c_3}(e^{c_3}{c}_1+e^t)-c_1}+e^{-c_3}(e^{c_3}{c}_1+e^t)+2c_1\log (e^{-c_3}(e^{c_3}{c}_1+e^t)-c_1)),z(t)\to -e^{-c_3}(e^{c_3}{c}_1+e^t)+c_2(e^{-c_3}(e^{c_3}{c}_1+e^t)-c_1)+(e^{-c_3}(e^{c_3}{c}_1+e^t)-c_1)(-\frac{c_1^2}{e^{-c_3}(e^{c_3}{c}_1+e^t)-c_1}+e^{-c_3}(e^{c_3}{c}_1+e^t)+2c_1\log (e^{-c_3}(e^{c_3}{c}_1+e^t)-c_1))+c_1\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 45 $$\{[\{x\left(t\right)=\mathit{\_}\mathit{C}\mathit{2}+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^t\},\{y\left(t\right)=(\int {\left(x\left(t\right)\right)}^2{\mathrm{e}}^{-t}\mathrm{d}t+\mathit{\_}\mathit{C}\mathit{1}){\mathrm{e}}^t\},\{z\left(t\right)=-\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+y\left(t\right)\}]\}$$