10.43   ODE No. 1898

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

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

Mathematica: cpu = 0.037505 (sec), leaf count = 420 $$\left\{\{x(t)\to -\frac{1}{5}{c}_1{e}^{\frac{t}{2}-\frac{\sqrt{5}t}{2}}(\sqrt{5}{e}^{\sqrt{5}t}-5e^{\frac{\sqrt{5}t}{2}+\frac{t}{2}}-\sqrt{5})+\frac{c_2{e}^{\frac{t}{2}-\frac{\sqrt{5}t}{2}}(e^{\sqrt{5}t}-1)}{\sqrt{5}}-\frac{1}{10}{c}_4{e}^{\frac{t}{2}-\frac{\sqrt{5}t}{2}}(5e^{\sqrt{5}t}+\sqrt{5}{e}^{\sqrt{5}t}-10e^{\frac{\sqrt{5}t}{2}+\frac{t}{2}}+5-\sqrt{5}),y(t)\to -\frac{1}{10}{c}_1{e}^{-\frac{\sqrt{5}t}{2}}(-5e^{t/2}-\sqrt{5}{e}^{t/2}+10e^{\frac{\sqrt{5}t}{2}}-5e^{\sqrt{5}t+\frac{t}{2}}+\sqrt{5}{e}^{\sqrt{5}t+\frac{t}{2}})+\frac{1}{10}{c}_2{e}^{-\frac{\sqrt{5}t}{2}}(-5e^{t/2}-\sqrt{5}{e}^{t/2}+10e^{\frac{\sqrt{5}t}{2}}-5e^{\sqrt{5}t+\frac{t}{2}}+\sqrt{5}{e}^{\sqrt{5}t+\frac{t}{2}})+\frac{c_4{e}^{\frac{t}{2}-\frac{\sqrt{5}t}{2}}(e^{\sqrt{5}t}-1)}{\sqrt{5}}+c_3\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 73 $$\left\{\{x\left(t\right)=(-\frac{1}{2}-\frac{\sqrt{5}}{2})\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{\frac{(\sqrt{5}+1)t}{2}}+(\frac{\sqrt{5}}{2}-\frac{1}{2})\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{-\frac{(\sqrt{5}-1)t}{2}}+\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^t,y\left(t\right)=\mathit{\_}\mathit{C}\mathit{2}+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{\frac{(\sqrt{5}+1)t}{2}}+\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{-\frac{(\sqrt{5}-1)t}{2}}\}\right\}$$