ODE No. 1908

$$\{x^{\prime }(t)=6x(t)-72y(t)+44z(t),y^{\prime }(t)=4x(t)-4y(t)+26z(t),z^{\prime }(t)=6x(t)-63y(t)+38z(t)\}$$ ✓ Mathematica : cpu = 0.0344443 (sec), leaf count = 551

DSolve[{Derivative[1][x][t] == 6*x[t] - 72*y[t] + 44*z[t], Derivative[1][y][t] == 4*x[t] - 4*y[t] + 26*z[t], Derivative[1][z][t] == 6*x[t] - 63*y[t] + 38*z[t]},{x[t], y[t], z[t]},t]
 

$$\left\{\{x(t)\to -36c_2\text{RootSum}[{\mathrm{\#}\text{1}}^3-40{\mathrm{\#}\text{1}}^2+1714\mathrm{\#}\text{1}+1404\mathrm{\&},\frac{2\mathrm{\#}\text{1}{e}^{\mathrm{\#}\text{1}t}+e^{\mathrm{\#}\text{1}t}}{3{\mathrm{\#}\text{1}}^2-80\mathrm{\#}\text{1}+1714}\mathrm{\&}]+4c_3\text{RootSum}[{\mathrm{\#}\text{1}}^3-40{\mathrm{\#}\text{1}}^2+1714\mathrm{\#}\text{1}+1404\mathrm{\&},\frac{11\mathrm{\#}\text{1}{e}^{\mathrm{\#}\text{1}t}-424e^{\mathrm{\#}\text{1}t}}{3{\mathrm{\#}\text{1}}^2-80\mathrm{\#}\text{1}+1714}\mathrm{\&}]+c_1\text{RootSum}[{\mathrm{\#}\text{1}}^3-40{\mathrm{\#}\text{1}}^2+1714\mathrm{\#}\text{1}+1404\mathrm{\&},\frac{{\mathrm{\#}\text{1}}^2{e}^{\mathrm{\#}\text{1}t}-34\mathrm{\#}\text{1}{e}^{\mathrm{\#}\text{1}t}+1486e^{\mathrm{\#}\text{1}t}}{3{\mathrm{\#}\text{1}}^2-80\mathrm{\#}\text{1}+1714}\mathrm{\&}],y(t)\to 4c_1\text{RootSum}[{\mathrm{\#}\text{1}}^3-40{\mathrm{\#}\text{1}}^2+1714\mathrm{\#}\text{1}+1404\mathrm{\&},\frac{\mathrm{\#}\text{1}{e}^{\mathrm{\#}\text{1}t}+e^{\mathrm{\#}\text{1}t}}{3{\mathrm{\#}\text{1}}^2-80\mathrm{\#}\text{1}+1714}\mathrm{\&}]+2c_3\text{RootSum}[{\mathrm{\#}\text{1}}^3-40{\mathrm{\#}\text{1}}^2+1714\mathrm{\#}\text{1}+1404\mathrm{\&},\frac{13\mathrm{\#}\text{1}{e}^{\mathrm{\#}\text{1}t}+10e^{\mathrm{\#}\text{1}t}}{3{\mathrm{\#}\text{1}}^2-80\mathrm{\#}\text{1}+1714}\mathrm{\&}]+c_2\text{RootSum}[{\mathrm{\#}\text{1}}^3-40{\mathrm{\#}\text{1}}^2+1714\mathrm{\#}\text{1}+1404\mathrm{\&},\frac{{\mathrm{\#}\text{1}}^2{e}^{\mathrm{\#}\text{1}t}-44\mathrm{\#}\text{1}{e}^{\mathrm{\#}\text{1}t}-36e^{\mathrm{\#}\text{1}t}}{3{\mathrm{\#}\text{1}}^2-80\mathrm{\#}\text{1}+1714}\mathrm{\&}],z(t)\to 6c_1\text{RootSum}[{\mathrm{\#}\text{1}}^3-40{\mathrm{\#}\text{1}}^2+1714\mathrm{\#}\text{1}+1404\mathrm{\&},\frac{\mathrm{\#}\text{1}{e}^{\mathrm{\#}\text{1}t}-38e^{\mathrm{\#}\text{1}t}}{3{\mathrm{\#}\text{1}}^2-80\mathrm{\#}\text{1}+1714}\mathrm{\&}]-9c_2\text{RootSum}[{\mathrm{\#}\text{1}}^3-40{\mathrm{\#}\text{1}}^2+1714\mathrm{\#}\text{1}+1404\mathrm{\&},\frac{7\mathrm{\#}\text{1}{e}^{\mathrm{\#}\text{1}t}+6e^{\mathrm{\#}\text{1}t}}{3{\mathrm{\#}\text{1}}^2-80\mathrm{\#}\text{1}+1714}\mathrm{\&}]+c_3\text{RootSum}[{\mathrm{\#}\text{1}}^3-40{\mathrm{\#}\text{1}}^2+1714\mathrm{\#}\text{1}+1404\mathrm{\&},\frac{{\mathrm{\#}\text{1}}^2{e}^{\mathrm{\#}\text{1}t}-2\mathrm{\#}\text{1}{e}^{\mathrm{\#}\text{1}t}+264e^{\mathrm{\#}\text{1}t}}{3{\mathrm{\#}\text{1}}^2-80\mathrm{\#}\text{1}+1714}\mathrm{\&}]\}\right\}$$ ✓ Maple : cpu = 1.155 (sec), leaf count = 1129

dsolve({diff(x(t),t) = 6*x(t)-72*y(t)+44*z(t), diff(y(t),t) = 4*x(t)-4*y(t)+26*z(t), diff(z(t),t) = 6*x(t)-63*y(t)+38*z(t)})
 

$$\{x\left(t\right)=c_2{\mathrm{e}}^{\frac{(-3542+{(263474+18\sqrt{351406311})}^{\frac{2}{3}}+80{(263474+18\sqrt{351406311})}^{\frac{1}{3}})t}{6{(263474+18\sqrt{351406311})}^{\frac{1}{3}}}}\sin \left(\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}+3542)t\sqrt{3}{4}^{\frac{1}{3}}{(131737+9\sqrt{351406311})}^{\frac{2}{3}}}{1580844+108\sqrt{351406311}}\right)+c_3{\mathrm{e}}^{\frac{(-3542+{(263474+18\sqrt{351406311})}^{\frac{2}{3}}+80{(263474+18\sqrt{351406311})}^{\frac{1}{3}})t}{6{(263474+18\sqrt{351406311})}^{\frac{1}{3}}}}\cos \left(\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}+3542)t\sqrt{3}{4}^{\frac{1}{3}}{(131737+9\sqrt{351406311})}^{\frac{2}{3}}}{1580844+108\sqrt{351406311}}\right)+c_1{\mathrm{e}}^{-\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}-40{(263474+18\sqrt{351406311})}^{\frac{1}{3}}-3542)t}{3{(263474+18\sqrt{351406311})}^{\frac{1}{3}}}},y\left(t\right)=\frac{26522496((-\frac{29521(\sqrt{3}+\frac{3\sqrt{117135437}}{29521})c_2{\left((91637096720+4742532\sqrt{351406311}){(131737+9\sqrt{351406311})}^2\right)}^{\frac{1}{3}}}{133952}+c_3(\sqrt{351406311}+\frac{131737}{9}){(263474+18\sqrt{351406311})}^{\frac{1}{3}}+\frac{c_3(\sqrt{351406311}+\frac{131737}{9}){(263474+18\sqrt{351406311})}^{\frac{4}{3}}}{267904}-\frac{1612830834397c_3}{736736}+\frac{711c_3\sqrt{351406311}{(22909274180+1185633\sqrt{351406311})}^{\frac{1}{3}}}{8372}+\frac{10407223{(263474+18\sqrt{351406311})}^{\frac{2}{3}}{c}_3}{16744}-\frac{75104333c_3\sqrt{351406311}}{736736}-\frac{1612830834397c_2\sqrt{3}}{736736}-\frac{225312999c_2\sqrt{117135437}}{736736})\cos \left(\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}+3542)t\sqrt{3}{(22909274180+1185633\sqrt{351406311})}^{\frac{1}{3}}}{790422+54\sqrt{351406311}}\right)+(\frac{29521c_3(\sqrt{3}+\frac{3\sqrt{117135437}}{29521}){\left((91637096720+4742532\sqrt{351406311}){(131737+9\sqrt{351406311})}^2\right)}^{\frac{1}{3}}}{133952}+c_2(\sqrt{351406311}+\frac{131737}{9}){(263474+18\sqrt{351406311})}^{\frac{1}{3}}+\frac{c_2(\sqrt{351406311}+\frac{131737}{9}){(263474+18\sqrt{351406311})}^{\frac{4}{3}}}{267904}-\frac{1612830834397c_2}{736736}+\frac{711c_2\sqrt{351406311}{(22909274180+1185633\sqrt{351406311})}^{\frac{1}{3}}}{8372}+\frac{10407223{(263474+18\sqrt{351406311})}^{\frac{2}{3}}{c}_2}{16744}-\frac{75104333c_2\sqrt{351406311}}{736736}+\frac{1612830834397c_3\sqrt{3}}{736736}+\frac{225312999c_3\sqrt{117135437}}{736736})\sin \left(\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}+3542)t\sqrt{3}{(22909274180+1185633\sqrt{351406311})}^{\frac{1}{3}}}{790422+54\sqrt{351406311}}\right)){\mathrm{e}}^{\frac{(-3542+{(263474+18\sqrt{351406311})}^{\frac{2}{3}}+80{(263474+18\sqrt{351406311})}^{\frac{1}{3}})t}{6{(263474+18\sqrt{351406311})}^{\frac{1}{3}}}}-53044992{\mathrm{e}}^{-\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}-40{(263474+18\sqrt{351406311})}^{\frac{1}{3}}-3542)t}{3{(263474+18\sqrt{351406311})}^{\frac{1}{3}}}}{c}_1(-\frac{711{(131737+9\sqrt{351406311})}^{\frac{2}{3}}{4}^{\frac{1}{3}}\sqrt{351406311}}{33488}+(\sqrt{351406311}+\frac{131737}{9}){(263474+18\sqrt{351406311})}^{\frac{1}{3}}+(\frac{\sqrt{351406311}}{267904}+\frac{131737}{2411136}){(263474+18\sqrt{351406311})}^{\frac{4}{3}}-\frac{10407223{(263474+18\sqrt{351406311})}^{\frac{2}{3}}}{33488}-\frac{75104333\sqrt{351406311}}{736736}-\frac{1612830834397}{736736})}{{(263474+18\sqrt{351406311})}^{\frac{2}{3}}(73329029784+5009688\sqrt{351406311})},z\left(t\right)=-\frac{1322937(((\frac{38827(\sqrt{3}+\frac{18\sqrt{117135437}}{38827})c_2{\left((91637096720+4742532\sqrt{351406311}){(131737+9\sqrt{351406311})}^2\right)}^{\frac{1}{3}}}{440979}+c_3(\sqrt{351406311}+\frac{131737}{9}){(263474+18\sqrt{351406311})}^{\frac{1}{3}}-\frac{c_3(\sqrt{351406311}+\frac{131737}{9}){(263474+18\sqrt{351406311})}^{\frac{4}{3}}}{146993}-\frac{1818560275316c_3}{440979}-\frac{33060c_3\sqrt{351406311}{(22909274180+1185633\sqrt{351406311})}^{\frac{1}{3}}}{146993}-\frac{725870870{(263474+18\sqrt{351406311})}^{\frac{2}{3}}{c}_3}{440979}-\frac{34414106c_3\sqrt{351406311}}{146993}-\frac{1818560275316c_2\sqrt{3}}{440979}-\frac{103242318c_2\sqrt{117135437}}{146993})\cos \left(\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}+3542)t\sqrt{3}{(22909274180+1185633\sqrt{351406311})}^{\frac{1}{3}}}{790422+54\sqrt{351406311}}\right)+(-\frac{38827c_3(\sqrt{3}+\frac{18\sqrt{117135437}}{38827}){\left((91637096720+4742532\sqrt{351406311}){(131737+9\sqrt{351406311})}^2\right)}^{\frac{1}{3}}}{440979}+c_2(\sqrt{351406311}+\frac{131737}{9}){(263474+18\sqrt{351406311})}^{\frac{1}{3}}-\frac{c_2(\sqrt{351406311}+\frac{131737}{9}){(263474+18\sqrt{351406311})}^{\frac{4}{3}}}{146993}-\frac{1818560275316c_2}{440979}-\frac{33060c_2\sqrt{351406311}{(22909274180+1185633\sqrt{351406311})}^{\frac{1}{3}}}{146993}-\frac{725870870{(263474+18\sqrt{351406311})}^{\frac{2}{3}}{c}_2}{440979}-\frac{34414106c_2\sqrt{351406311}}{146993}+\frac{1818560275316c_3\sqrt{3}}{440979}+\frac{103242318c_3\sqrt{117135437}}{146993})\sin \left(\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}+3542)t\sqrt{3}{(22909274180+1185633\sqrt{351406311})}^{\frac{1}{3}}}{790422+54\sqrt{351406311}}\right)){\mathrm{e}}^{\frac{(-3542+{(263474+18\sqrt{351406311})}^{\frac{2}{3}}+80{(263474+18\sqrt{351406311})}^{\frac{1}{3}})t}{6{(263474+18\sqrt{351406311})}^{\frac{1}{3}}}}-2{\mathrm{e}}^{-\frac{({(263474+18\sqrt{351406311})}^{\frac{2}{3}}-40{(263474+18\sqrt{351406311})}^{\frac{1}{3}}-3542)t}{3{(263474+18\sqrt{351406311})}^{\frac{1}{3}}}}{c}_1(\frac{8265{(131737+9\sqrt{351406311})}^{\frac{2}{3}}{4}^{\frac{1}{3}}\sqrt{351406311}}{146993}+(\sqrt{351406311}+\frac{131737}{9}){(263474+18\sqrt{351406311})}^{\frac{1}{3}}+(-\frac{\sqrt{351406311}}{146993}-\frac{131737}{1322937}){(263474+18\sqrt{351406311})}^{\frac{4}{3}}+\frac{362935435{(263474+18\sqrt{351406311})}^{\frac{2}{3}}}{440979}-\frac{34414106\sqrt{351406311}}{146993}-\frac{1818560275316}{440979}))}{{(263474+18\sqrt{351406311})}^{\frac{2}{3}}(4073834988+278316\sqrt{351406311})}\}$$