10.52   ODE No. 1907

$$\boxed{{\displaystyle \{\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)=-3x\left(t\right)+48y\left(t\right)-28z\left(t\right),\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)=-4x\left(t\right)+40y\left(t\right)-22z\left(t\right),\frac{\mathrm{d}}{\mathrm{d}t}z\left(t\right)=-6x\left(t\right)+57y\left(t\right)-31z\left(t\right)\}}}$$

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

Mathematica: cpu = 0.009501 (sec), leaf count = 179 $$\left\{\{x(t)\to c_1(-e^t)(2e^{2t}-3)+6c_2{e}^t(2e^t+3e^{2t}-5)-2c_3{e}^t(4e^t+5e^{2t}-9),y(t)\to -2c_1{e}^t(e^{2t}-1)+c_2{e}^t(3e^t+18e^{2t}-20)-2c_3{e}^t(e^t+5e^{2t}-6),z(t)\to -3c_1{e}^t(e^{2t}-1)+3c_2{e}^t(e^t+9e^{2t}-10)-c_3{e}^t(2e^t+15e^{2t}-18)\}\right\}$$

Maple: cpu = 0.046 (sec), leaf count = 66 $$\left\{\{x\left(t\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{3t}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{2t}+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^t,y\left(t\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{3t}+\frac{\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{2t}}{4}+\frac{2\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^t}{3},z\left(t\right)=\frac{3\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{3t}}{2}+\frac{\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{2t}}{4}+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^t\}\right\}$$