2.1906   ODE No. 1906

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

$$\{x^{\prime }(t)=x(t)+y(t)-z(t),y^{\prime }(t)=-x(t)+y(t)+z(t),z^{\prime }(t)=x(t)-y(t)+z(t)\}$$ ✓ Mathematica : cpu = 0.0501751 (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 = 0.073 (sec), leaf count = 128

$$\left\{\{x\left(t\right)={\mathrm{e}}^t(\sin \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{2}+\cos \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{3}+\mathit{\_}\mathit{C}\mathit{1}),y\left(t\right)=-\frac{{\mathrm{e}}^t(\sqrt{3}\sin \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{3}-\sqrt{3}\cos \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{2}+\sin \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{2}+\cos \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{3}-2\mathit{\_}\mathit{C}\mathit{1})}{2},z\left(t\right)=\frac{{\mathrm{e}}^t(\sqrt{3}\sin \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{3}-\sqrt{3}\cos \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{2}-\sin \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{2}-\cos \left(\sqrt{3}t\right)\mathit{\_}\mathit{C}\mathit{3}+2\mathit{\_}\mathit{C}\mathit{1})}{2}\}\right\}$$