10.53   ODE No. 1908

$$\boxed{{\displaystyle \{\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)=6x\left(t\right)-72y\left(t\right)+44z\left(t\right),\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)=4x\left(t\right)-4y\left(t\right)+26z\left(t\right),\frac{\mathrm{d}}{\mathrm{d}t}z\left(t\right)=6x\left(t\right)-63y\left(t\right)+38z\left(t\right)\}}}$$

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

Mathematica: cpu = 0.019502 (sec), leaf count = 551

Result too large for latex to process

Maple: cpu = 0.468 (sec), leaf count = 3207 $$\left\{\{x\left(t\right)=\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}+80\sqrt[3]{263474+18\sqrt{351406311}}-3542)t}{6\sqrt[3]{263474+18\sqrt{351406311}}}}\sin \left(\frac{t\sqrt{3}\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542\sqrt{3}t}{6\sqrt[3]{263474+18\sqrt{351406311}}}\right)+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}+80\sqrt[3]{263474+18\sqrt{351406311}}-3542)t}{6\sqrt[3]{263474+18\sqrt{351406311}}}}\cos \left(\frac{t\sqrt{3}\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542\sqrt{3}t}{6\sqrt[3]{263474+18\sqrt{351406311}}}\right)+\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}-40\sqrt[3]{263474+18\sqrt{351406311}}-3542)t}{3\sqrt[3]{263474+18\sqrt{351406311}}}},y\left(t\right)=-\frac{(99{(263474+18\sqrt{351406311})}^{4/3}\sqrt{351406311}+1449107{(263474+18\sqrt{351406311})}^{4/3}-563112\sqrt{351406311}\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+26522496\sqrt{351406311}\sqrt[3]{263474+18\sqrt{351406311}}-8242520616{(263474+18\sqrt{351406311})}^{2/3}-2703755988\sqrt{351406311}+388221561728\sqrt[3]{263474+18\sqrt{351406311}}-58061910038292)\mathit{\_}\mathit{C}\mathit{1}}{2504844\sqrt{351406311}\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+36664514892{(263474+18\sqrt{351406311})}^{2/3}}{\mathrm{e}}^{-\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}-40\sqrt[3]{263474+18\sqrt{351406311}}-3542)t}{3\sqrt[3]{263474+18\sqrt{351406311}}}}+(\frac{\mathit{\_}\mathit{C}\mathit{3}}{5009688\sqrt{351406311}\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+73329029784{(263474+18\sqrt{351406311})}^{2/3}}(99\sqrt{351406311}\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right){(263474+18\sqrt{351406311})}^{4/3}+1449107\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right){(263474+18\sqrt{351406311})}^{4/3}+1126224\sqrt{351406311}\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+26522496\sqrt{351406311}\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt[3]{263474+18\sqrt{351406311}}+5845158\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{3}\sqrt[3]{(91637096720+4742532\sqrt{351406311}){(131737+9\sqrt{351406311})}^2}+594\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{117135437}\sqrt[3]{(91637096720+4742532\sqrt{351406311}){(131737+9\sqrt{351406311})}^2}+16485041232\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right){(263474+18\sqrt{351406311})}^{2/3}-2703755988\sqrt{351406311}\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)[phone]\mathrm{}\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{3}+5918679936\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{117135437}+404352\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{41162131803542907}+730862676\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{1054218933}+388221561728\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt[3]{263474+18\sqrt{351406311}}-58061910038292\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right))+\frac{\mathit{\_}\mathit{C}\mathit{2}}{5009688\sqrt{351406311}\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+73329029784{(263474+18\sqrt{351406311})}^{2/3}}(99\sqrt{351406311}\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right){(263474+18\sqrt{351406311})}^{4/3}+1449107\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right){(263474+18\sqrt{351406311})}^{4/3}+1126224\sqrt{351406311}\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+26522496\sqrt{351406311}\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt[3]{263474+18\sqrt{351406311}}+16485041232\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right){(263474+18\sqrt{351406311})}^{2/3}-5845158\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{3}\sqrt[3]{(91637096720+4742532\sqrt{351406311}){(131737+9\sqrt{351406311})}^2}-594\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{117135437}\sqrt[3]{(91637096720+4742532\sqrt{351406311}){(131737+9\sqrt{351406311})}^2}-2703755988\sqrt{351406311}\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)[phone]\mathrm{}\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt[3]{263474+18\sqrt{351406311}}-10697961816468\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{3}-5918679936\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{117135437}-404352\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{41162131803542907}-730862676\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{1054218933}-58061910038292\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right))){\mathrm{e}}^{\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}+80\sqrt[3]{263474+18\sqrt{351406311}}-3542)t}{6\sqrt[3]{263474+18\sqrt{351406311}}}},z\left(t\right)=-\frac{(9{(263474+18\sqrt{351406311})}^{4/3}\sqrt{351406311}+131737{(263474+18\sqrt{351406311})}^{4/3}-74385\sqrt{351406311}\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}-1322937\sqrt{351406311}\sqrt[3]{263474+18\sqrt{351406311}}-1088806305{(263474+18\sqrt{351406311})}^{2/3}+309726954\sqrt{351406311}-19364416841\sqrt[3]{263474+18\sqrt{351406311}}+5455680825948)\mathit{\_}\mathit{C}\mathit{1}}{139158\sqrt{351406311}\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+2036917494{(263474+18\sqrt{351406311})}^{2/3}}{\mathrm{e}}^{-\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}-40\sqrt[3]{263474+18\sqrt{351406311}}-3542)t}{3\sqrt[3]{263474+18\sqrt{351406311}}}}+(\frac{\mathit{\_}\mathit{C}\mathit{3}}{278316\sqrt{351406311}\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+4073834988{(263474+18\sqrt{351406311})}^{2/3}}(9\sqrt{351406311}\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right){(263474+18\sqrt{351406311})}^{4/3}+131737\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right){(263474+18\sqrt{351406311})}^{4/3}+148770\sqrt{351406311}\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}-1322937\sqrt{351406311}\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt[3]{263474+18\sqrt{351406311}}+116481\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{3}\sqrt[3]{(91637096720+4742532\sqrt{351406311}){(131737+9\sqrt{351406311})}^2}+54\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{117135437}\sqrt[3]{(91637096720+4742532\sqrt{351406311}){(131737+9\sqrt{351406311})}^2}+2177612610\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right){(263474+18\sqrt{351406311})}^{2/3}+309726954\sqrt{351406311}\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)-3093176197095\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{3}-295222617\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{117135437}-20169\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{41162131803542907}-211319415\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{1054218933}-19364416841\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt[3]{263474+18\sqrt{351406311}}+5455680825948\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right))+\frac{\mathit{\_}\mathit{C}\mathit{2}}{278316\sqrt{351406311}\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+4073834988{(263474+18\sqrt{351406311})}^{2/3}}(9\sqrt{351406311}\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right){(263474+18\sqrt{351406311})}^{4/3}+131737\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right){(263474+18\sqrt{351406311})}^{4/3}+148770\sqrt{351406311}\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}-1322937\sqrt{351406311}\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt[3]{263474+18\sqrt{351406311}}+2177612610\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right){(263474+18\sqrt{351406311})}^{2/3}-116481\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{3}\sqrt[3]{(91637096720+4742532\sqrt{351406311}){(131737+9\sqrt{351406311})}^2}-54\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{117135437}\sqrt[3]{(91637096720+4742532\sqrt{351406311}){(131737+9\sqrt{351406311})}^2}+309726954\sqrt{351406311}\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)-19364416841\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt[3]{263474+18\sqrt{351406311}}+3093176197095\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{3}+295222617\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{117135437}+20169\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{41162131803542907}+211319415\cos \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right)\sqrt{1054218933}+5455680825948\sin \left(1/6\frac{\sqrt{3}t(\sqrt[3]{4}\sqrt[3]{{(131737+9\sqrt{351406311})}^2}+3542)}{\sqrt[3]{263474+18\sqrt{351406311}}}\right))){\mathrm{e}}^{\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}+80\sqrt[3]{263474+18\sqrt{351406311}}-3542)t}{6\sqrt[3]{263474+18\sqrt{351406311}}}}\}\right\}$$