\[ \left \{x'(t)=6 x(t)-72 y(t)+44 z(t),y'(t)=4 x(t)-4 y(t)+26 z(t),z'(t)=6 x(t)-63 y(t)+38 z(t)\right \} \] ✓ 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 \{\left \{x(t)\to -36 c_2 \text {RootSum}\left [\text {$\#$1}^3-40 \text {$\#$1}^2+1714 \text {$\#$1}+1404\& ,\frac {2 \text {$\#$1} e^{\text {$\#$1} t}+e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-80 \text {$\#$1}+1714}\& \right ]+4 c_3 \text {RootSum}\left [\text {$\#$1}^3-40 \text {$\#$1}^2+1714 \text {$\#$1}+1404\& ,\frac {11 \text {$\#$1} e^{\text {$\#$1} t}-424 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-80 \text {$\#$1}+1714}\& \right ]+c_1 \text {RootSum}\left [\text {$\#$1}^3-40 \text {$\#$1}^2+1714 \text {$\#$1}+1404\& ,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}-34 \text {$\#$1} e^{\text {$\#$1} t}+1486 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-80 \text {$\#$1}+1714}\& \right ],y(t)\to 4 c_1 \text {RootSum}\left [\text {$\#$1}^3-40 \text {$\#$1}^2+1714 \text {$\#$1}+1404\& ,\frac {\text {$\#$1} e^{\text {$\#$1} t}+e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-80 \text {$\#$1}+1714}\& \right ]+2 c_3 \text {RootSum}\left [\text {$\#$1}^3-40 \text {$\#$1}^2+1714 \text {$\#$1}+1404\& ,\frac {13 \text {$\#$1} e^{\text {$\#$1} t}+10 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-80 \text {$\#$1}+1714}\& \right ]+c_2 \text {RootSum}\left [\text {$\#$1}^3-40 \text {$\#$1}^2+1714 \text {$\#$1}+1404\& ,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}-44 \text {$\#$1} e^{\text {$\#$1} t}-36 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-80 \text {$\#$1}+1714}\& \right ],z(t)\to 6 c_1 \text {RootSum}\left [\text {$\#$1}^3-40 \text {$\#$1}^2+1714 \text {$\#$1}+1404\& ,\frac {\text {$\#$1} e^{\text {$\#$1} t}-38 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-80 \text {$\#$1}+1714}\& \right ]-9 c_2 \text {RootSum}\left [\text {$\#$1}^3-40 \text {$\#$1}^2+1714 \text {$\#$1}+1404\& ,\frac {7 \text {$\#$1} e^{\text {$\#$1} t}+6 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-80 \text {$\#$1}+1714}\& \right ]+c_3 \text {RootSum}\left [\text {$\#$1}^3-40 \text {$\#$1}^2+1714 \text {$\#$1}+1404\& ,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}-2 \text {$\#$1} e^{\text {$\#$1} t}+264 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-80 \text {$\#$1}+1714}\& \right ]\right \}\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)})
\[\left \{x \left (t \right ) = c_{2} {\mathrm e}^{\frac {\left (-3542+\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}+80 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}\right ) t}{6 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}}} \sin \left (\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}+3542\right ) t \sqrt {3}\, 4^{\frac {1}{3}} \left (131737+9 \sqrt {351406311}\right )^{\frac {2}{3}}}{1580844+108 \sqrt {351406311}}\right )+c_{3} {\mathrm e}^{\frac {\left (-3542+\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}+80 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}\right ) t}{6 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}}} \cos \left (\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}+3542\right ) t \sqrt {3}\, 4^{\frac {1}{3}} \left (131737+9 \sqrt {351406311}\right )^{\frac {2}{3}}}{1580844+108 \sqrt {351406311}}\right )+c_{1} {\mathrm e}^{-\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}-40 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}-3542\right ) t}{3 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}}}, y \left (t \right ) = \frac {26522496 \left (\left (-\frac {29521 \left (\sqrt {3}+\frac {3 \sqrt {117135437}}{29521}\right ) c_{2} \left (\left (91637096720+4742532 \sqrt {351406311}\right ) \left (131737+9 \sqrt {351406311}\right )^{2}\right )^{\frac {1}{3}}}{133952}+c_{3} \left (\sqrt {351406311}+\frac {131737}{9}\right ) \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}+\frac {c_{3} \left (\sqrt {351406311}+\frac {131737}{9}\right ) \left (263474+18 \sqrt {351406311}\right )^{\frac {4}{3}}}{267904}-\frac {1612830834397 c_{3}}{736736}+\frac {711 c_{3} \sqrt {351406311}\, \left (22909274180+1185633 \sqrt {351406311}\right )^{\frac {1}{3}}}{8372}+\frac {10407223 \left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}} c_{3}}{16744}-\frac {75104333 c_{3} \sqrt {351406311}}{736736}-\frac {1612830834397 c_{2} \sqrt {3}}{736736}-\frac {225312999 c_{2} \sqrt {117135437}}{736736}\right ) \cos \left (\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}+3542\right ) t \sqrt {3}\, \left (22909274180+1185633 \sqrt {351406311}\right )^{\frac {1}{3}}}{790422+54 \sqrt {351406311}}\right )+\left (\frac {29521 c_{3} \left (\sqrt {3}+\frac {3 \sqrt {117135437}}{29521}\right ) \left (\left (91637096720+4742532 \sqrt {351406311}\right ) \left (131737+9 \sqrt {351406311}\right )^{2}\right )^{\frac {1}{3}}}{133952}+c_{2} \left (\sqrt {351406311}+\frac {131737}{9}\right ) \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}+\frac {c_{2} \left (\sqrt {351406311}+\frac {131737}{9}\right ) \left (263474+18 \sqrt {351406311}\right )^{\frac {4}{3}}}{267904}-\frac {1612830834397 c_{2}}{736736}+\frac {711 c_{2} \sqrt {351406311}\, \left (22909274180+1185633 \sqrt {351406311}\right )^{\frac {1}{3}}}{8372}+\frac {10407223 \left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}} c_{2}}{16744}-\frac {75104333 c_{2} \sqrt {351406311}}{736736}+\frac {1612830834397 c_{3} \sqrt {3}}{736736}+\frac {225312999 c_{3} \sqrt {117135437}}{736736}\right ) \sin \left (\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}+3542\right ) t \sqrt {3}\, \left (22909274180+1185633 \sqrt {351406311}\right )^{\frac {1}{3}}}{790422+54 \sqrt {351406311}}\right )\right ) {\mathrm e}^{\frac {\left (-3542+\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}+80 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}\right ) t}{6 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}}}-53044992 \,{\mathrm e}^{-\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}-40 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}-3542\right ) t}{3 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}}} c_{1} \left (-\frac {711 \left (131737+9 \sqrt {351406311}\right )^{\frac {2}{3}} 4^{\frac {1}{3}} \sqrt {351406311}}{33488}+\left (\sqrt {351406311}+\frac {131737}{9}\right ) \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}+\left (\frac {\sqrt {351406311}}{267904}+\frac {131737}{2411136}\right ) \left (263474+18 \sqrt {351406311}\right )^{\frac {4}{3}}-\frac {10407223 \left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}}{33488}-\frac {75104333 \sqrt {351406311}}{736736}-\frac {1612830834397}{736736}\right )}{\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}} \left (73329029784+5009688 \sqrt {351406311}\right )}, z \left (t \right ) = -\frac {1322937 \left (\left (\left (\frac {38827 \left (\sqrt {3}+\frac {18 \sqrt {117135437}}{38827}\right ) c_{2} \left (\left (91637096720+4742532 \sqrt {351406311}\right ) \left (131737+9 \sqrt {351406311}\right )^{2}\right )^{\frac {1}{3}}}{440979}+c_{3} \left (\sqrt {351406311}+\frac {131737}{9}\right ) \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}-\frac {c_{3} \left (\sqrt {351406311}+\frac {131737}{9}\right ) \left (263474+18 \sqrt {351406311}\right )^{\frac {4}{3}}}{146993}-\frac {1818560275316 c_{3}}{440979}-\frac {33060 c_{3} \sqrt {351406311}\, \left (22909274180+1185633 \sqrt {351406311}\right )^{\frac {1}{3}}}{146993}-\frac {725870870 \left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}} c_{3}}{440979}-\frac {34414106 c_{3} \sqrt {351406311}}{146993}-\frac {1818560275316 c_{2} \sqrt {3}}{440979}-\frac {103242318 c_{2} \sqrt {117135437}}{146993}\right ) \cos \left (\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}+3542\right ) t \sqrt {3}\, \left (22909274180+1185633 \sqrt {351406311}\right )^{\frac {1}{3}}}{790422+54 \sqrt {351406311}}\right )+\left (-\frac {38827 c_{3} \left (\sqrt {3}+\frac {18 \sqrt {117135437}}{38827}\right ) \left (\left (91637096720+4742532 \sqrt {351406311}\right ) \left (131737+9 \sqrt {351406311}\right )^{2}\right )^{\frac {1}{3}}}{440979}+c_{2} \left (\sqrt {351406311}+\frac {131737}{9}\right ) \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}-\frac {c_{2} \left (\sqrt {351406311}+\frac {131737}{9}\right ) \left (263474+18 \sqrt {351406311}\right )^{\frac {4}{3}}}{146993}-\frac {1818560275316 c_{2}}{440979}-\frac {33060 c_{2} \sqrt {351406311}\, \left (22909274180+1185633 \sqrt {351406311}\right )^{\frac {1}{3}}}{146993}-\frac {725870870 \left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}} c_{2}}{440979}-\frac {34414106 c_{2} \sqrt {351406311}}{146993}+\frac {1818560275316 c_{3} \sqrt {3}}{440979}+\frac {103242318 c_{3} \sqrt {117135437}}{146993}\right ) \sin \left (\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}+3542\right ) t \sqrt {3}\, \left (22909274180+1185633 \sqrt {351406311}\right )^{\frac {1}{3}}}{790422+54 \sqrt {351406311}}\right )\right ) {\mathrm e}^{\frac {\left (-3542+\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}+80 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}\right ) t}{6 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}}}-2 \,{\mathrm e}^{-\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}-40 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}-3542\right ) t}{3 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}}} c_{1} \left (\frac {8265 \left (131737+9 \sqrt {351406311}\right )^{\frac {2}{3}} 4^{\frac {1}{3}} \sqrt {351406311}}{146993}+\left (\sqrt {351406311}+\frac {131737}{9}\right ) \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}+\left (-\frac {\sqrt {351406311}}{146993}-\frac {131737}{1322937}\right ) \left (263474+18 \sqrt {351406311}\right )^{\frac {4}{3}}+\frac {362935435 \left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}}{440979}-\frac {34414106 \sqrt {351406311}}{146993}-\frac {1818560275316}{440979}\right )\right )}{\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}} \left (4073834988+278316 \sqrt {351406311}\right )}\right \}\]