\[ \left \{x'(t)=6 x(t)-72 y(t)+44 z(t),y'(t)=4 x(t)-4 y(t)+26 z(t),z'(t)=6 x(t)-63 y(t)+38 z(t)\right \} \] ✓ Mathematica : cpu = 0.0235574 (sec), leaf count = 551
\[\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 = 0.745 (sec), leaf count = 1213
\[ \left \{ \left \{ x \left ( t \right ) ={\it \_C2}\,{{\rm e}^{{\frac { \left ( \left ( 263474+18\,\sqrt {351406311} \right ) ^{{\frac {2}{3}}}+80\,\sqrt [3]{263474+18\,\sqrt {351406311}}-3542 \right ) t}{6\,\sqrt [3]{263474+18\,\sqrt {351406311}}}}}}\sin \left ( {\frac {\sqrt {3}t \left ( \sqrt [3]{4}\sqrt [3]{ \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}+3542 \right ) }{6\,\sqrt [3]{263474+18\,\sqrt {351406311}}}} \right ) +{\it \_C3}\,{{\rm e}^{{\frac { \left ( \left ( 263474+18\,\sqrt {351406311} \right ) ^{{\frac {2}{3}}}+80\,\sqrt [3]{263474+18\,\sqrt {351406311}}-3542 \right ) t}{6\,\sqrt [3]{263474+18\,\sqrt {351406311}}}}}}\cos \left ( {\frac {\sqrt {3}t \left ( \sqrt [3]{4}\sqrt [3]{ \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}+3542 \right ) }{6\,\sqrt [3]{263474+18\,\sqrt {351406311}}}} \right ) +{\it \_C1}\,{{\rm e}^{-{\frac { \left ( \left ( 263474+18\,\sqrt {351406311} \right ) ^{{\frac {2}{3}}}-40\,\sqrt [3]{263474+18\,\sqrt {351406311}}-3542 \right ) t}{3\,\sqrt [3]{263474+18\,\sqrt {351406311}}}}}},y \left ( t \right ) ={\frac {1}{5009688\,\sqrt {351406311}\sqrt [3]{4}\sqrt [3]{ \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}+73329029784\, \left ( 263474+18\,\sqrt {351406311} \right ) ^{2/3}} \left ( \left ( \left ( -5845158\,{\it \_C2}\, \left ( \sqrt {3}+{\frac {3\,\sqrt {117135437}}{29521}} \right ) \sqrt [3]{ \left ( 91637096720+4742532\,\sqrt {351406311} \right ) \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}+1126224\,{\it \_C3}\,\sqrt {351406311}\sqrt [3]{4}\sqrt [3]{ \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}+26522496\,{\it \_C3}\, \left ( \sqrt {351406311}+{\frac {131737}{9}} \right ) \sqrt [3]{263474+18\,\sqrt {351406311}}+ \left ( 99\,{\it \_C3}\,\sqrt {351406311}+1449107\,{\it \_C3} \right ) \left ( 263474+18\,\sqrt {351406311} \right ) ^{{\frac {4}{3}}}-404352\,{\it \_C2}\,\sqrt {41162131803542907}+16485041232\,{\it \_C3}\, \left ( 263474+18\,\sqrt {351406311} \right ) ^{2/3}-10697961816468\,\sqrt {3}{\it \_C2}-5918679936\,{\it \_C2}\,\sqrt {117135437}-730862676\,{\it \_C2}\,\sqrt {1054218933}-2703755988\,{\it \_C3}\,\sqrt {351406311}-58061910038292\,{\it \_C3} \right ) \cos \left ( {\frac {\sqrt {3}t \left ( \sqrt [3]{4}\sqrt [3]{ \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}+3542 \right ) }{6\,\sqrt [3]{263474+18\,\sqrt {351406311}}}} \right ) +404352\,\sin \left ( 1/6\,{\frac {\sqrt {3}t \left ( \sqrt [3]{4}\sqrt [3]{ \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}+3542 \right ) }{\sqrt [3]{263474+18\,\sqrt {351406311}}}} \right ) \left ( {\frac {324731\,{\it \_C3}\, \left ( \sqrt {3}+{\frac {3\,\sqrt {117135437}}{29521}} \right ) \sqrt [3]{ \left ( 91637096720+4742532\,\sqrt {351406311} \right ) \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}}{22464}}+{\frac {869\,{\it \_C2}\,\sqrt {351406311}\sqrt [3]{4}\sqrt [3]{ \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}}{312}}+{\frac {1771\,{\it \_C2}\, \left ( \sqrt {351406311}+{\frac {131737}{9}} \right ) \sqrt [3]{263474+18\,\sqrt {351406311}}}{27}}+{\frac {11\,{\it \_C2}\, \left ( \sqrt {351406311}+{\frac {131737}{9}} \right ) \left ( 263474+18\,\sqrt {351406311} \right ) ^{4/3}}{44928}}+{\it \_C3}\,\sqrt {41162131803542907}+{\frac {114479453\, \left ( 263474+18\,\sqrt {351406311} \right ) ^{2/3}{\it \_C2}}{2808}}-{\frac {75104333\,{\it \_C2}\,\sqrt {351406311}}{11232}}+{\frac {297165606013\,\sqrt {3}{\it \_C3}}{11232}}+{\frac {131737\,{\it \_C3}\,\sqrt {117135437}}{9}}+{\frac {2255749\,{\it \_C3}\,\sqrt {1054218933}}{1248}}-{\frac {1612830834397\,{\it \_C2}}{11232}} \right ) \right ) {{\rm e}^{{\frac { \left ( \left ( 263474+18\,\sqrt {351406311} \right ) ^{{\frac {2}{3}}}+80\,\sqrt [3]{263474+18\,\sqrt {351406311}}-3542 \right ) t}{6\,\sqrt [3]{263474+18\,\sqrt {351406311}}}}}}-53044992\,{{\rm e}^{-1/3\,{\frac { \left ( \left ( 263474+18\,\sqrt {351406311} \right ) ^{2/3}-40\,\sqrt [3]{263474+18\,\sqrt {351406311}}-3542 \right ) t}{\sqrt [3]{263474+18\,\sqrt {351406311}}}}}}{\it \_C1}\, \left ( -{\frac {711\,\sqrt {351406311}\sqrt [3]{4}\sqrt [3]{ \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}}{33488}}+ \left ( \sqrt {351406311}+{\frac {131737}{9}} \right ) \sqrt [3]{263474+18\,\sqrt {351406311}}+ \left ( {\frac {\sqrt {351406311}}{267904}}+{\frac {131737}{2411136}} \right ) \left ( 263474+18\,\sqrt {351406311} \right ) ^{4/3}-{\frac {10407223\, \left ( 263474+18\,\sqrt {351406311} \right ) ^{2/3}}{33488}}-{\frac {75104333\,\sqrt {351406311}}{736736}}-{\frac {1612830834397}{736736}} \right ) \right ) },z \left ( t \right ) ={\frac {1}{278316\,\sqrt {351406311}\sqrt [3]{4}\sqrt [3]{ \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}+4073834988\, \left ( 263474+18\,\sqrt {351406311} \right ) ^{2/3}} \left ( \left ( \left ( -116481\,{\it \_C2}\, \left ( \sqrt {3}+{\frac {18\,\sqrt {117135437}}{38827}} \right ) \sqrt [3]{ \left ( 91637096720+4742532\,\sqrt {351406311} \right ) \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}+148770\,{\it \_C3}\,\sqrt {351406311}\sqrt [3]{4}\sqrt [3]{ \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}-1322937\,{\it \_C3}\, \left ( \sqrt {351406311}+{\frac {131737}{9}} \right ) \sqrt [3]{263474+18\,\sqrt {351406311}}+ \left ( 9\,{\it \_C3}\,\sqrt {351406311}+131737\,{\it \_C3} \right ) \left ( 263474+18\,\sqrt {351406311} \right ) ^{{\frac {4}{3}}}+20169\,{\it \_C2}\,\sqrt {41162131803542907}+2177612610\,{\it \_C3}\, \left ( 263474+18\,\sqrt {351406311} \right ) ^{2/3}+3093176197095\,\sqrt {3}{\it \_C2}+295222617\,{\it \_C2}\,\sqrt {117135437}+211319415\,{\it \_C2}\,\sqrt {1054218933}+309726954\,{\it \_C3}\,\sqrt {351406311}+5455680825948\,{\it \_C3} \right ) \cos \left ( {\frac {\sqrt {3}t \left ( \sqrt [3]{4}\sqrt [3]{ \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}+3542 \right ) }{6\,\sqrt [3]{263474+18\,\sqrt {351406311}}}} \right ) -20169\,\sin \left ( 1/6\,{\frac {\sqrt {3}t \left ( \sqrt [3]{4}\sqrt [3]{ \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}+3542 \right ) }{\sqrt [3]{263474+18\,\sqrt {351406311}}}} \right ) \left ( -{\frac { \left ( 38827\,\sqrt {3}+18\,\sqrt {117135437} \right ) {\it \_C3}\,\sqrt [3]{ \left ( 91637096720+4742532\,\sqrt {351406311} \right ) \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}}{6723}}-{\frac {5510\,{\it \_C2}\,\sqrt {351406311}\sqrt [3]{4}\sqrt [3]{ \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}}{747}}+{\frac {1771\,{\it \_C2}\, \left ( \sqrt {351406311}+{\frac {131737}{9}} \right ) \sqrt [3]{263474+18\,\sqrt {351406311}}}{27}}-{\frac {{\it \_C2}\, \left ( \sqrt {351406311}+{\frac {131737}{9}} \right ) \left ( 263474+18\,\sqrt {351406311} \right ) ^{4/3}}{2241}}+{\it \_C3}\,\sqrt {41162131803542907}-{\frac {725870870\, \left ( 263474+18\,\sqrt {351406311} \right ) ^{2/3}{\it \_C2}}{6723}}-{\frac {34414106\,{\it \_C2}\,\sqrt {351406311}}{2241}}+{\frac {1031058732365\,\sqrt {3}{\it \_C3}}{6723}}+{\frac {131737\,{\it \_C3}\,\sqrt {117135437}}{9}}+{\frac {7826645\,{\it \_C3}\,\sqrt {1054218933}}{747}}-{\frac {1818560275316\,{\it \_C2}}{6723}} \right ) \right ) {{\rm e}^{{\frac { \left ( \left ( 263474+18\,\sqrt {351406311} \right ) ^{{\frac {2}{3}}}+80\,\sqrt [3]{263474+18\,\sqrt {351406311}}-3542 \right ) t}{6\,\sqrt [3]{263474+18\,\sqrt {351406311}}}}}}+2645874\, \left ( {\frac {8265\,\sqrt {351406311}\sqrt [3]{4}\sqrt [3]{ \left ( 131737+9\,\sqrt {351406311} \right ) ^{2}}}{146993}}+ \left ( \sqrt {351406311}+{\frac {131737}{9}} \right ) \sqrt [3]{263474+18\,\sqrt {351406311}}+ \left ( -{\frac {\sqrt {351406311}}{146993}}-{\frac {131737}{1322937}} \right ) \left ( 263474+18\,\sqrt {351406311} \right ) ^{4/3}+{\frac {362935435\, \left ( 263474+18\,\sqrt {351406311} \right ) ^{2/3}}{440979}}-{\frac {34414106\,\sqrt {351406311}}{146993}}-{\frac {1818560275316}{440979}} \right ) {{\rm e}^{-1/3\,{\frac { \left ( \left ( 263474+18\,\sqrt {351406311} \right ) ^{2/3}-40\,\sqrt [3]{263474+18\,\sqrt {351406311}}-3542 \right ) t}{\sqrt [3]{263474+18\,\sqrt {351406311}}}}}}{\it \_C1} \right ) } \right \} \right \} \]