10.45   ODE No. 1900

$$\boxed{{\displaystyle \{\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)=4x\left(t\right),\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)=x\left(t\right)-2y\left(t\right),\frac{\mathrm{d}}{\mathrm{d}t}z\left(t\right)=x\left(t\right)-4y\left(t\right)+z\left(t\right)\}}}$$

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

Mathematica: cpu = 0.009501 (sec), leaf count = 94 $$\left\{\{x(t)\to c_1{e}^{4t},y(t)\to \frac{1}{6}{c}_1{e}^{-2t}(e^{6t}-1)+c_2{e}^{-2t},z(t)\to \frac{1}{9}{c}_1{e}^{-2t}(e^{3t}+e^{6t}-2)-\frac{4}{3}{c}_2{e}^{-2t}(e^{3t}-1)+c_3{e}^t\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 50 $$\left\{\{x\left(t\right)=\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{4t},y\left(t\right)=\frac{\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{4t}}{6}+{\mathrm{e}}^{-2t}\mathit{\_}\mathit{C}\mathit{2},z\left(t\right)=\frac{\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{4t}}{9}+\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^t+\frac{4{\mathrm{e}}^{-2t}\mathit{\_}\mathit{C}\mathit{2}}{3}\}\right\}$$