60.9.52 problem 1908
Internal
problem
ID
[11831]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
8,
system
of
first
order
odes
Problem
number
:
1908
Date
solved
:
Sunday, March 30, 2025 at 09:16:17 PM
CAS
classification
:
system_of_ODEs
\begin{align*} \frac {d}{d t}x \left (t \right )&=6 x \left (t \right )-72 y \left (t \right )+44 z \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=4 x \left (t \right )-4 y \left (t \right )+26 z \left (t \right )\\ \frac {d}{d t}z \left (t \right )&=6 x \left (t \right )-63 y \left (t \right )+38 z \left (t \right ) \end{align*}
✓ Maple. Time used: 0.370 (sec). Leaf size: 3112
ode:=[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)];
dsolve(ode);
\begin{align*}
x \left (t \right ) &= \cos \left (\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{{2}/{3}}+3542\right ) t \sqrt {3}\, 4^{{1}/{3}}}{12 \left (131737+9 \sqrt {351406311}\right )^{{1}/{3}}}\right ) {\mathrm e}^{\frac {\left (-3542+\left (263474+18 \sqrt {351406311}\right )^{{2}/{3}}+80 \left (263474+18 \sqrt {351406311}\right )^{{1}/{3}}\right ) t}{6 \left (263474+18 \sqrt {351406311}\right )^{{1}/{3}}}} c_3 +\sin \left (\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{{2}/{3}}+3542\right ) t \sqrt {3}\, 4^{{1}/{3}}}{12 \left (131737+9 \sqrt {351406311}\right )^{{1}/{3}}}\right ) {\mathrm e}^{\frac {\left (-3542+\left (263474+18 \sqrt {351406311}\right )^{{2}/{3}}+80 \left (263474+18 \sqrt {351406311}\right )^{{1}/{3}}\right ) t}{6 \left (263474+18 \sqrt {351406311}\right )^{{1}/{3}}}} c_2 +c_1 \,{\mathrm e}^{-\frac {\left (\left (263474+18 \sqrt {351406311}\right )^{{2}/{3}}-40 \left (263474+18 \sqrt {351406311}\right )^{{1}/{3}}-3542\right ) t}{3 \left (263474+18 \sqrt {351406311}\right )^{{1}/{3}}}} \\
\text {Expression too large to display} \\
\text {Expression too large to display} \\
\end{align*}
✓ Mathematica. Time used: 0.033 (sec). Leaf size: 551
ode={D[x[t],t]==6*x[t]-72*y[t]+44*z[t],D[y[t],t]==4*x[t]-4*y[t]+26*z[t],D[z[t],t]==6*x[t]-63*y[t]+38*z[t]};
ic={};
DSolve[{ode,ic},{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*}
✗ Sympy
from sympy import *
t = symbols("t")
x = Function("x")
y = Function("y")
z = Function("z")
ode=[Eq(-6*x(t) + 72*y(t) - 44*z(t) + Derivative(x(t), t),0),Eq(-4*x(t) + 4*y(t) - 26*z(t) + Derivative(y(t), t),0),Eq(-6*x(t) + 63*y(t) - 38*z(t) + Derivative(z(t), t),0)]
ics = {}
dsolve(ode,func=[x(t),y(t),z(t)],ics=ics)
Timed Out