10.27   ODE No. 1882

$$\boxed{{\displaystyle \{\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)+\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)-2y\left(t\right)={\mathrm{e}}^{2t},2\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)-3x\left(t\right)=0\}}}$$

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

Mathematica: cpu = 0.419553 (sec), leaf count = 928 $$\left\{\{x(t)\to \frac{1}{46}{e}^{t/2}{c}_1(23\cos \left(\frac{\sqrt{23}t}{2}\right)+23e^{t/2}-3\sqrt{23}\sin \left(\frac{\sqrt{23}t}{2}\right))+\frac{e^{3t/2}(23e^{t/2}\cos \left(\frac{\sqrt{23}t}{2}\right)-7\sqrt{23}{e}^{t/2}\sin \left(\frac{\sqrt{23}t}{2}\right)+46)(23\cos \left(\frac{\sqrt{23}t}{2}\right)+23e^{t/2}-3\sqrt{23}\sin \left(\frac{\sqrt{23}t}{2}\right))}{12696}+\frac{1}{69}{e}^{t/2}{c}_3(-23\cos \left(\frac{\sqrt{23}t}{2}\right)+23e^{t/2}-\sqrt{23}\sin \left(\frac{\sqrt{23}t}{2}\right))+\frac{1}{138}{e}^{t/2}{c}_2(-23\cos \left(\frac{\sqrt{23}t}{2}\right)+23e^{t/2}+11\sqrt{23}\sin \left(\frac{\sqrt{23}t}{2}\right))+\frac{e^{3t/2}(-23\cos \left(\frac{\sqrt{23}t}{2}\right)+23e^{t/2}+11\sqrt{23}\sin \left(\frac{\sqrt{23}t}{2}\right))(46e^{t/2}\cos \left(\frac{\sqrt{23}t}{2}\right)+4\sqrt{23}{e}^{t/2}\sin \left(\frac{\sqrt{23}t}{2}\right)+23)}{19044}+\frac{e^{3t/2}(-23\cos \left(\frac{\sqrt{23}t}{2}\right)+23e^{t/2}-\sqrt{23}\sin \left(\frac{\sqrt{23}t}{2}\right))(-161e^{t/2}\cos \left(\frac{\sqrt{23}t}{2}\right)+13\sqrt{23}{e}^{t/2}\sin \left(\frac{\sqrt{23}t}{2}\right)+92)}{38088},y(t)\to \frac{1}{138}{e}^{t/2}{c}_2(-23\cos \left(\frac{\sqrt{23}t}{2}\right)+23e^{t/2}-25\sqrt{23}\sin \left(\frac{\sqrt{23}t}{2}\right))+\frac{e^{3t/2}(46e^{t/2}\cos \left(\frac{\sqrt{23}t}{2}\right)+4\sqrt{23}{e}^{t/2}\sin \left(\frac{\sqrt{23}t}{2}\right)+23)(-23\cos \left(\frac{\sqrt{23}t}{2}\right)+23e^{t/2}-25\sqrt{23}\sin \left(\frac{\sqrt{23}t}{2}\right))}{19044}+\frac{1}{69}{e}^{t/2}{c}_3(46\cos \left(\frac{\sqrt{23}t}{2}\right)+23e^{t/2}-4\sqrt{23}\sin \left(\frac{\sqrt{23}t}{2}\right))+\frac{1}{46}{e}^{t/2}{c}_1(-23\cos \left(\frac{\sqrt{23}t}{2}\right)+23e^{t/2}+11\sqrt{23}\sin \left(\frac{\sqrt{23}t}{2}\right))+\frac{e^{3t/2}(-23\cos \left(\frac{\sqrt{23}t}{2}\right)+23e^{t/2}+11\sqrt{23}\sin \left(\frac{\sqrt{23}t}{2}\right))(23e^{t/2}\cos \left(\frac{\sqrt{23}t}{2}\right)-7\sqrt{23}{e}^{t/2}\sin \left(\frac{\sqrt{23}t}{2}\right)+46)}{12696}+\frac{e^{3t/2}(46\cos \left(\frac{\sqrt{23}t}{2}\right)+23e^{t/2}-4\sqrt{23}\sin \left(\frac{\sqrt{23}t}{2}\right))(-161e^{t/2}\cos \left(\frac{\sqrt{23}t}{2}\right)+13\sqrt{23}{e}^{t/2}\sin \left(\frac{\sqrt{23}t}{2}\right)+92)}{38088}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 118 $$\left\{\{x\left(t\right)=\frac{{\mathrm{e}}^{2t}}{4}+\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^t+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\frac{t}{2}}\cos \left(\frac{\sqrt{23}t}{2}\right)+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{\frac{t}{2}}\sin \left(\frac{\sqrt{23}t}{2}\right),y\left(t\right)=-\frac{{\mathrm{e}}^{2t}}{8}+\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^t-\frac{7\mathit{\_}\mathit{C}\mathit{2}}{4}{\mathrm{e}}^{\frac{t}{2}}\cos \left(\frac{\sqrt{23}t}{2}\right)+\frac{\mathit{\_}\mathit{C}\mathit{2}\sqrt{23}}{4}{\mathrm{e}}^{\frac{t}{2}}\sin \left(\frac{\sqrt{23}t}{2}\right)-\frac{7\mathit{\_}\mathit{C}\mathit{3}}{4}{\mathrm{e}}^{\frac{t}{2}}\sin \left(\frac{\sqrt{23}t}{2}\right)-\frac{\mathit{\_}\mathit{C}\mathit{3}\sqrt{23}}{4}{\mathrm{e}}^{\frac{t}{2}}\cos \left(\frac{\sqrt{23}t}{2}\right)\}\right\}$$