10.31   ODE No. 1886

$$\boxed{{\displaystyle \{\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)+ay\left(t\right)=0,\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}y\left(t\right)-a^{2}y\left(t\right)=0\}}}$$

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

Mathematica: cpu = 0.021003 (sec), leaf count = 115 $$\left\{\{x(t)\to -\frac{c_4{e}^{-at}(-2at{e}^{at}+e^{2at}-1)}{2a^2}-\frac{c_3{e}^{-at}{(e^{at}-1)}^2}{2a}+c_{2}t+c_1,y(t)\to \frac{1}{2}{c}_3{e}^{-at}(e^{2at}+1)+\frac{c_4{e}^{-at}(e^{2at}-1)}{2a}\}\right\}$$

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