2.1898   ODE No. 1898

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

$$\{-x^{\prime }(t)+x^{″}(t)+y^{\prime }(t)=0,x^{″}(t)-x(t)+y^{″}(t)=0\}$$ ✓ Mathematica : cpu = 0.0248989 (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 = 0.195 (sec), leaf count = 71

$$\left\{\{x\left(t\right)=\frac{\mathit{\_}\mathit{C}\mathit{4}(\sqrt{5}-1)}{2}{\mathrm{e}}^{-\frac{(\sqrt{5}-1)t}{2}}-\frac{\mathit{\_}\mathit{C}\mathit{3}(\sqrt{5}+1)}{2}{\mathrm{e}}^{\frac{(\sqrt{5}+1)t}{2}}+\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^t,y\left(t\right)=\mathit{\_}\mathit{C}\mathit{2}+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{\frac{(\sqrt{5}+1)t}{2}}+\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{-\frac{(\sqrt{5}-1)t}{2}}\}\right\}$$