Internal problem ID [9487]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1908.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=6 x \relax (t )-72 y \relax (t )+44 z \relax (t )\\ y^{\prime }\relax (t )&=4 x \relax (t )-4 y \relax (t )+26 z \relax (t )\\ z^{\prime }\relax (t )&=6 x \relax (t )-63 y \relax (t )+38 z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.828 (sec). Leaf size: 2967
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(t), y(t), z(t)}, singsol=all)
\[ x \relax (t ) = c_{2} {\mathrm e}^{\frac {\left (-3542+\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}+80 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}\right ) t}{6 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}}} \sin \left (\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}+3542\right ) t \sqrt {3}\, 4^{\frac {1}{3}}}{12 \left (131737+9 \sqrt {351406311}\right )^{\frac {1}{3}}}\right )+c_{3} {\mathrm e}^{\frac {\left (-3542+\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}+80 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}\right ) t}{6 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}}} \cos \left (\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}+3542\right ) t \sqrt {3}\, 4^{\frac {1}{3}}}{12 \left (131737+9 \sqrt {351406311}\right )^{\frac {1}{3}}}\right )+c_{1} {\mathrm e}^{-\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{\frac {2}{3}}-40 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}-3542\right ) t}{3 \left (263474+18 \sqrt {351406311}\right )^{\frac {1}{3}}}} \] \[ \text {Expression too large to display} \] \[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 551
DSolve[{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]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} 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 ] \\ \end{align*}