10.51   ODE No. 1906

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

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

Mathematica: cpu = 0.052007 (sec), leaf count = 278 $$\left\{\{x(t)\to \frac{1}{3}{c}_1{e}^t(2\cos \left(\sqrt{3}t\right)+1)-\frac{1}{3}{c}_2{e}^t(-\sqrt{3}\sin \left(\sqrt{3}t\right)+\cos \left(\sqrt{3}t\right)-1)-\frac{1}{3}{c}_3{e}^t(\sqrt{3}\sin \left(\sqrt{3}t\right)+\cos \left(\sqrt{3}t\right)-1),y(t)\to \frac{1}{3}{c}_2{e}^t(2\cos \left(\sqrt{3}t\right)+1)-\frac{1}{3}{c}_3{e}^t(-\sqrt{3}\sin \left(\sqrt{3}t\right)+\cos \left(\sqrt{3}t\right)-1)-\frac{1}{3}{c}_1{e}^t(\sqrt{3}\sin \left(\sqrt{3}t\right)+\cos \left(\sqrt{3}t\right)-1),z(t)\to \frac{1}{3}{c}_3{e}^t(2\cos \left(\sqrt{3}t\right)+1)-\frac{1}{3}{c}_1{e}^t(-\sqrt{3}\sin \left(\sqrt{3}t\right)+\cos \left(\sqrt{3}t\right)-1)-\frac{1}{3}{c}_2{e}^t(\sqrt{3}\sin \left(\sqrt{3}t\right)+\cos \left(\sqrt{3}t\right)-1)\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 128 $$\left\{\{x\left(t\right)={\mathrm{e}}^t(\sin \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{2}+\cos \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{3}+\mathit{\_}\mathit{C}\mathit{1}),y\left(t\right)=-\frac{{\mathrm{e}}^t(\sin \left(\sqrt{3}t\right)\sqrt{3}\mathit{\_}\mathit{C}\mathit{3}-\cos \left(\sqrt{3}t\right)\sqrt{3}\mathit{\_}\mathit{C}\mathit{2}+\sin \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{2}+\cos \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{3}-2\mathit{\_}\mathit{C}\mathit{1})}{2},z\left(t\right)=\frac{{\mathrm{e}}^t(\sin \left(\sqrt{3}t\right)\sqrt{3}\mathit{\_}\mathit{C}\mathit{3}-\cos \left(\sqrt{3}t\right)\sqrt{3}\mathit{\_}\mathit{C}\mathit{2}-\sin \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{2}-\cos \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{3}+2\mathit{\_}\mathit{C}\mathit{1})}{2}\}\right\}$$