10.40   ODE No. 1895

$$\boxed{{\displaystyle \{\mathit{a}\mathit{11}\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)+\mathit{b}\mathit{11}\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+\mathit{c}\mathit{11}x\left(t\right)+\mathit{a}\mathit{12}\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}y\left(t\right)+\mathit{b}\mathit{12}\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)+\mathit{c}\mathit{12}y\left(t\right)=0,\mathit{a}\mathit{21}\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)+\mathit{b}\mathit{21}\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+\mathit{c}\mathit{21}x\left(t\right)+\mathit{a}\mathit{22}\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}y\left(t\right)+\mathit{b}\mathit{22}\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)+\mathit{c}\mathit{22}y\left(t\right)=0\}}}$$

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

Mathematica: cpu = 0.449557 (sec), leaf count = 7517

Result too large for latex to process

Maple: cpu = 0.156 (sec), leaf count = 1187 $$\left\{\{x\left(t\right)=\sum _{\mathit{\_}\mathit{a}=1}^4{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}((\mathit{a}\mathit{22}\mathit{a}\mathit{11}-\mathit{a}\mathit{12}\mathit{a}\mathit{21}){\mathit{\_}\mathit{Z}}^4+(\mathit{a}\mathit{11}\mathit{b}\mathit{22}-\mathit{a}\mathit{12}\mathit{b}\mathit{21}-\mathit{a}\mathit{21}\mathit{b}\mathit{12}+\mathit{a}\mathit{22}\mathit{b}\mathit{11}){\mathit{\_}\mathit{Z}}^3+(\mathit{a}\mathit{11}\mathit{c}\mathit{22}-\mathit{a}\mathit{12}\mathit{c}\mathit{21}-\mathit{a}\mathit{21}\mathit{c}\mathit{12}+\mathit{a}\mathit{22}\mathit{c}\mathit{11}+\mathit{b}\mathit{11}\mathit{b}\mathit{22}-\mathit{b}\mathit{21}\mathit{b}\mathit{12}){\mathit{\_}\mathit{Z}}^2+(\mathit{b}\mathit{11}\mathit{c}\mathit{22}-\mathit{c}\mathit{21}\mathit{b}\mathit{12}-\mathit{b}\mathit{21}\mathit{c}\mathit{12}+\mathit{b}\mathit{22}\mathit{c}\mathit{11})\mathit{\_}\mathit{Z}+\mathit{c}\mathit{11}\mathit{c}\mathit{22}-\mathit{c}\mathit{12}\mathit{c}\mathit{21},\mathit{i}\mathit{n}\mathit{d}\mathit{e}\mathit{x}=\mathit{\_}\mathit{a})t}{\mathit{\_}\mathit{C}}_{\mathit{\_}\mathit{a}},y\left(t\right)=-\frac{((\mathit{a}\mathit{11}\mathit{a}\mathit{12}\mathit{a}\mathit{22}-{\mathit{a}\mathit{12}}^2\mathit{a}\mathit{21})\mathit{b}\mathit{22}+(-\mathit{a}\mathit{11}{\mathit{a}\mathit{22}}^2+\mathit{a}\mathit{12}\mathit{a}\mathit{21}\mathit{a}\mathit{22})\mathit{b}\mathit{12})\sum _{\mathit{\_}\mathit{a}=1}^4{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}((\mathit{a}\mathit{22}\mathit{a}\mathit{11}-\mathit{a}\mathit{12}\mathit{a}\mathit{21}){\mathit{\_}\mathit{Z}}^4+(\mathit{a}\mathit{11}\mathit{b}\mathit{22}-\mathit{a}\mathit{12}\mathit{b}\mathit{21}-\mathit{a}\mathit{21}\mathit{b}\mathit{12}+\mathit{a}\mathit{22}\mathit{b}\mathit{11}){\mathit{\_}\mathit{Z}}^3+(\mathit{a}\mathit{11}\mathit{c}\mathit{22}-\mathit{a}\mathit{12}\mathit{c}\mathit{21}-\mathit{a}\mathit{21}\mathit{c}\mathit{12}+\mathit{a}\mathit{22}\mathit{c}\mathit{11}+\mathit{b}\mathit{11}\mathit{b}\mathit{22}-\mathit{b}\mathit{21}\mathit{b}\mathit{12}){\mathit{\_}\mathit{Z}}^2+(\mathit{b}\mathit{11}\mathit{c}\mathit{22}-\mathit{c}\mathit{21}\mathit{b}\mathit{12}-\mathit{b}\mathit{21}\mathit{c}\mathit{12}+\mathit{b}\mathit{22}\mathit{c}\mathit{11})\mathit{\_}\mathit{Z}+\mathit{c}\mathit{11}\mathit{c}\mathit{22}-\mathit{c}\mathit{12}\mathit{c}\mathit{21},\mathit{i}\mathit{n}\mathit{d}\mathit{e}\mathit{x}=\mathit{\_}\mathit{a})\right)}^3{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}((\mathit{a}\mathit{22}\mathit{a}\mathit{11}-\mathit{a}\mathit{12}\mathit{a}\mathit{21}){\mathit{\_}\mathit{Z}}^4+(\mathit{a}\mathit{11}\mathit{b}\mathit{22}-\mathit{a}\mathit{12}\mathit{b}\mathit{21}-\mathit{a}\mathit{21}\mathit{b}\mathit{12}+\mathit{a}\mathit{22}\mathit{b}\mathit{11}){\mathit{\_}\mathit{Z}}^3+(\mathit{a}\mathit{11}\mathit{c}\mathit{22}-\mathit{a}\mathit{12}\mathit{c}\mathit{21}-\mathit{a}\mathit{21}\mathit{c}\mathit{12}+\mathit{a}\mathit{22}\mathit{c}\mathit{11}+\mathit{b}\mathit{11}\mathit{b}\mathit{22}-\mathit{b}\mathit{21}\mathit{b}\mathit{12}){\mathit{\_}\mathit{Z}}^2+(\mathit{b}\mathit{11}\mathit{c}\mathit{22}-\mathit{c}\mathit{21}\mathit{b}\mathit{12}-\mathit{b}\mathit{21}\mathit{c}\mathit{12}+\mathit{b}\mathit{22}\mathit{c}\mathit{11})\mathit{\_}\mathit{Z}+\mathit{c}\mathit{11}\mathit{c}\mathit{22}-\mathit{c}\mathit{12}\mathit{c}\mathit{21},\mathit{i}\mathit{n}\mathit{d}\mathit{e}\mathit{x}=\mathit{\_}\mathit{a})t}{\mathit{\_}\mathit{C}}_{\mathit{\_}\mathit{a}}}{{\mathit{a}\mathit{12}}^2{\mathit{c}\mathit{22}}^2+(-2\mathit{a}\mathit{12}\mathit{a}\mathit{22}\mathit{c}\mathit{12}-\mathit{a}\mathit{12}\mathit{b}\mathit{12}\mathit{b}\mathit{22}+\mathit{a}\mathit{22}{\mathit{b}\mathit{12}}^2)\mathit{c}\mathit{22}+{\mathit{c}\mathit{12}}^2{\mathit{a}\mathit{22}}^2+(\mathit{a}\mathit{12}{\mathit{b}\mathit{22}}^2-\mathit{a}\mathit{22}\mathit{b}\mathit{12}\mathit{b}\mathit{22})\mathit{c}\mathit{12}}-\frac{((-\mathit{a}\mathit{11}\mathit{a}\mathit{12}\mathit{a}\mathit{22}+{\mathit{a}\mathit{12}}^2\mathit{a}\mathit{21})\mathit{c}\mathit{22}+(\mathit{a}\mathit{11}{\mathit{a}\mathit{22}}^2-\mathit{a}\mathit{12}\mathit{a}\mathit{21}\mathit{a}\mathit{22})\mathit{c}\mathit{12}+\mathit{a}\mathit{11}\mathit{a}\mathit{12}{\mathit{b}\mathit{22}}^2+(-{\mathit{a}\mathit{12}}^2\mathit{b}\mathit{21}+(-\mathit{a}\mathit{22}\mathit{a}\mathit{11}-\mathit{a}\mathit{12}\mathit{a}\mathit{21})\mathit{b}\mathit{12}+\mathit{a}\mathit{12}\mathit{a}\mathit{22}\mathit{b}\mathit{11})\mathit{b}\mathit{22}+\mathit{a}\mathit{12}\mathit{a}\mathit{22}\mathit{b}\mathit{12}\mathit{b}\mathit{21}+\mathit{a}\mathit{21}\mathit{a}\mathit{22}{\mathit{b}\mathit{12}}^2-{\mathit{a}\mathit{22}}^2\mathit{b}\mathit{11}\mathit{b}\mathit{12})\sum _{\mathit{\_}\mathit{a}=1}^4{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}((\mathit{a}\mathit{22}\mathit{a}\mathit{11}-\mathit{a}\mathit{12}\mathit{a}\mathit{21}){\mathit{\_}\mathit{Z}}^4+(\mathit{a}\mathit{11}\mathit{b}\mathit{22}-\mathit{a}\mathit{12}\mathit{b}\mathit{21}-\mathit{a}\mathit{21}\mathit{b}\mathit{12}+\mathit{a}\mathit{22}\mathit{b}\mathit{11}){\mathit{\_}\mathit{Z}}^3+(\mathit{a}\mathit{11}\mathit{c}\mathit{22}-\mathit{a}\mathit{12}\mathit{c}\mathit{21}-\mathit{a}\mathit{21}\mathit{c}\mathit{12}+\mathit{a}\mathit{22}\mathit{c}\mathit{11}+\mathit{b}\mathit{11}\mathit{b}\mathit{22}-\mathit{b}\mathit{21}\mathit{b}\mathit{12}){\mathit{\_}\mathit{Z}}^2+(\mathit{b}\mathit{11}\mathit{c}\mathit{22}-\mathit{c}\mathit{21}\mathit{b}\mathit{12}-\mathit{b}\mathit{21}\mathit{c}\mathit{12}+\mathit{b}\mathit{22}\mathit{c}\mathit{11})\mathit{\_}\mathit{Z}+\mathit{c}\mathit{11}\mathit{c}\mathit{22}-\mathit{c}\mathit{12}\mathit{c}\mathit{21},\mathit{i}\mathit{n}\mathit{d}\mathit{e}\mathit{x}=\mathit{\_}\mathit{a})\right)}^2{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}((\mathit{a}\mathit{22}\mathit{a}\mathit{11}-\mathit{a}\mathit{12}\mathit{a}\mathit{21}){\mathit{\_}\mathit{Z}}^4+(\mathit{a}\mathit{11}\mathit{b}\mathit{22}-\mathit{a}\mathit{12}\mathit{b}\mathit{21}-\mathit{a}\mathit{21}\mathit{b}\mathit{12}+\mathit{a}\mathit{22}\mathit{b}\mathit{11}){\mathit{\_}\mathit{Z}}^3+(\mathit{a}\mathit{11}\mathit{c}\mathit{22}-\mathit{a}\mathit{12}\mathit{c}\mathit{21}-\mathit{a}\mathit{21}\mathit{c}\mathit{12}+\mathit{a}\mathit{22}\mathit{c}\mathit{11}+\mathit{b}\mathit{11}\mathit{b}\mathit{22}-\mathit{b}\mathit{21}\mathit{b}\mathit{12}){\mathit{\_}\mathit{Z}}^2+(\mathit{b}\mathit{11}\mathit{c}\mathit{22}-\mathit{c}\mathit{21}\mathit{b}\mathit{12}-\mathit{b}\mathit{21}\mathit{c}\mathit{12}+\mathit{b}\mathit{22}\mathit{c}\mathit{11})\mathit{\_}\mathit{Z}+\mathit{c}\mathit{11}\mathit{c}\mathit{22}-\mathit{c}\mathit{12}\mathit{c}\mathit{21},\mathit{i}\mathit{n}\mathit{d}\mathit{e}\mathit{x}=\mathit{\_}\mathit{a})t}{\mathit{\_}\mathit{C}}_{\mathit{\_}\mathit{a}}}{{\mathit{a}\mathit{12}}^2{\mathit{c}\mathit{22}}^2+(-2\mathit{a}\mathit{12}\mathit{a}\mathit{22}\mathit{c}\mathit{12}-\mathit{a}\mathit{12}\mathit{b}\mathit{12}\mathit{b}\mathit{22}+\mathit{a}\mathit{22}{\mathit{b}\mathit{12}}^2)\mathit{c}\mathit{22}+{\mathit{c}\mathit{12}}^2{\mathit{a}\mathit{22}}^2+(\mathit{a}\mathit{12}{\mathit{b}\mathit{22}}^2-\mathit{a}\mathit{22}\mathit{b}\mathit{12}\mathit{b}\mathit{22})\mathit{c}\mathit{12}}-\frac{(({\mathit{a}\mathit{12}}^2\mathit{b}\mathit{21}-\mathit{a}\mathit{12}\mathit{a}\mathit{22}\mathit{b}\mathit{11})\mathit{c}\mathit{22}+(-{\mathit{a}\mathit{12}}^2\mathit{b}\mathit{22}+\mathit{a}\mathit{12}\mathit{a}\mathit{22}\mathit{b}\mathit{12})\mathit{c}\mathit{21}+(-\mathit{a}\mathit{12}\mathit{a}\mathit{22}\mathit{b}\mathit{21}+{\mathit{a}\mathit{22}}^2\mathit{b}\mathit{11})\mathit{c}\mathit{12}+(\mathit{a}\mathit{12}\mathit{a}\mathit{22}\mathit{b}\mathit{22}-{\mathit{a}\mathit{22}}^2\mathit{b}\mathit{12})\mathit{c}\mathit{11}+\mathit{a}\mathit{12}\mathit{b}\mathit{11}{\mathit{b}\mathit{22}}^2+(-\mathit{a}\mathit{12}\mathit{b}\mathit{12}\mathit{b}\mathit{21}-\mathit{a}\mathit{22}\mathit{b}\mathit{11}\mathit{b}\mathit{12})\mathit{b}\mathit{22}+\mathit{a}\mathit{22}\mathit{b}\mathit{21}{\mathit{b}\mathit{12}}^2)\sum _{\mathit{\_}\mathit{a}=1}^4\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}((\mathit{a}\mathit{22}\mathit{a}\mathit{11}-\mathit{a}\mathit{12}\mathit{a}\mathit{21}){\mathit{\_}\mathit{Z}}^4+(\mathit{a}\mathit{11}\mathit{b}\mathit{22}-\mathit{a}\mathit{12}\mathit{b}\mathit{21}-\mathit{a}\mathit{21}\mathit{b}\mathit{12}+\mathit{a}\mathit{22}\mathit{b}\mathit{11}){\mathit{\_}\mathit{Z}}^3+(\mathit{a}\mathit{11}\mathit{c}\mathit{22}-\mathit{a}\mathit{12}\mathit{c}\mathit{21}-\mathit{a}\mathit{21}\mathit{c}\mathit{12}+\mathit{a}\mathit{22}\mathit{c}\mathit{11}+\mathit{b}\mathit{11}\mathit{b}\mathit{22}-\mathit{b}\mathit{21}\mathit{b}\mathit{12}){\mathit{\_}\mathit{Z}}^2+(\mathit{b}\mathit{11}\mathit{c}\mathit{22}-\mathit{c}\mathit{21}\mathit{b}\mathit{12}-\mathit{b}\mathit{21}\mathit{c}\mathit{12}+\mathit{b}\mathit{22}\mathit{c}\mathit{11})\mathit{\_}\mathit{Z}+\mathit{c}\mathit{11}\mathit{c}\mathit{22}-\mathit{c}\mathit{12}\mathit{c}\mathit{21},\mathit{i}\mathit{n}\mathit{d}\mathit{e}\mathit{x}=\mathit{\_}\mathit{a}){\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}((\mathit{a}\mathit{22}\mathit{a}\mathit{11}-\mathit{a}\mathit{12}\mathit{a}\mathit{21}){\mathit{\_}\mathit{Z}}^4+(\mathit{a}\mathit{11}\mathit{b}\mathit{22}-\mathit{a}\mathit{12}\mathit{b}\mathit{21}-\mathit{a}\mathit{21}\mathit{b}\mathit{12}+\mathit{a}\mathit{22}\mathit{b}\mathit{11}){\mathit{\_}\mathit{Z}}^3+(\mathit{a}\mathit{11}\mathit{c}\mathit{22}-\mathit{a}\mathit{12}\mathit{c}\mathit{21}-\mathit{a}\mathit{21}\mathit{c}\mathit{12}+\mathit{a}\mathit{22}\mathit{c}\mathit{11}+\mathit{b}\mathit{11}\mathit{b}\mathit{22}-\mathit{b}\mathit{21}\mathit{b}\mathit{12}){\mathit{\_}\mathit{Z}}^2+(\mathit{b}\mathit{11}\mathit{c}\mathit{22}-\mathit{c}\mathit{21}\mathit{b}\mathit{12}-\mathit{b}\mathit{21}\mathit{c}\mathit{12}+\mathit{b}\mathit{22}\mathit{c}\mathit{11})\mathit{\_}\mathit{Z}+\mathit{c}\mathit{11}\mathit{c}\mathit{22}-\mathit{c}\mathit{12}\mathit{c}\mathit{21},\mathit{i}\mathit{n}\mathit{d}\mathit{e}\mathit{x}=\mathit{\_}\mathit{a})t}{\mathit{\_}\mathit{C}}_{\mathit{\_}\mathit{a}}}{{\mathit{a}\mathit{12}}^2{\mathit{c}\mathit{22}}^2+(-2\mathit{a}\mathit{12}\mathit{a}\mathit{22}\mathit{c}\mathit{12}-\mathit{a}\mathit{12}\mathit{b}\mathit{12}\mathit{b}\mathit{22}+\mathit{a}\mathit{22}{\mathit{b}\mathit{12}}^2)\mathit{c}\mathit{22}+{\mathit{c}\mathit{12}}^2{\mathit{a}\mathit{22}}^2+(\mathit{a}\mathit{12}{\mathit{b}\mathit{22}}^2-\mathit{a}\mathit{22}\mathit{b}\mathit{12}\mathit{b}\mathit{22})\mathit{c}\mathit{12}}-\frac{(({\mathit{a}\mathit{12}}^2\mathit{c}\mathit{21}-\mathit{a}\mathit{12}\mathit{a}\mathit{22}\mathit{c}\mathit{11})\mathit{c}\mathit{22}+(-\mathit{a}\mathit{12}\mathit{a}\mathit{22}\mathit{c}\mathit{12}-\mathit{a}\mathit{12}\mathit{b}\mathit{12}\mathit{b}\mathit{22}+\mathit{a}\mathit{22}{\mathit{b}\mathit{12}}^2)\mathit{c}\mathit{21}+{\mathit{a}\mathit{22}}^2\mathit{c}\mathit{11}\mathit{c}\mathit{12}+(\mathit{a}\mathit{12}{\mathit{b}\mathit{22}}^2-\mathit{a}\mathit{22}\mathit{b}\mathit{12}\mathit{b}\mathit{22})\mathit{c}\mathit{11})\sum 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