80.11.11 problem 11
Internal
problem
ID
[21419]
Book
:
A
Textbook
on
Ordinary
Differential
Equations
by
Shair
Ahmad
and
Antonio
Ambrosetti.
Second
edition.
ISBN
978-3-319-16407-6.
Springer
2015
Section
:
Chapter
12.
Stability
theory.
Excercise
12.6
at
page
270
Problem
number
:
11
Date
solved
:
Thursday, October 02, 2025 at 07:30:59 PM
CAS
classification
:
system_of_ODEs
\begin{align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{2} \left (t \right )-x_{3} \left (t \right ) \end{align*}
✓ Maple. Time used: 0.356 (sec). Leaf size: 2267
ode:=[diff(x__1(t),t) = x__1(t)+x__2(t)+x__3(t), diff(x__2(t),t) = x__1(t)-2*x__2(t)-x__3(t), diff(x__3(t),t) = x__2(t)-x__3(t)];
dsolve(ode);
\begin{align*} \text {Solution too large to show}\end{align*}
✓ Mathematica. Time used: 0.014 (sec). Leaf size: 519
ode={D[x1[t],t]==x1[t]+x2[t]+x3[t],D[x2[t],t]==x1[t]-2*x2[t]-x3[t],D[x3[t],t]==x2[t]-x3[t]};
ic={};
DSolve[{ode,ic},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions->True]
\begin{align*} \text {x1}(t)&\to c_3 \text {RootSum}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-5\&,\frac {\text {$\#$1} e^{\text {$\#$1} t}+e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+4 \text {$\#$1}-1}\&\right ]+c_2 \text {RootSum}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-5\&,\frac {\text {$\#$1} e^{\text {$\#$1} t}+2 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+4 \text {$\#$1}-1}\&\right ]+c_1 \text {RootSum}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-5\&,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}+3 \text {$\#$1} e^{\text {$\#$1} t}+3 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+4 \text {$\#$1}-1}\&\right ]\\ \text {x2}(t)&\to -c_3 \text {RootSum}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-5\&,\frac {\text {$\#$1} e^{\text {$\#$1} t}-2 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+4 \text {$\#$1}-1}\&\right ]+c_1 \text {RootSum}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-5\&,\frac {\text {$\#$1} e^{\text {$\#$1} t}+e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+4 \text {$\#$1}-1}\&\right ]+c_2 \text {RootSum}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-5\&,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}-e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+4 \text {$\#$1}-1}\&\right ]\\ \text {x3}(t)&\to c_1 \text {RootSum}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-5\&,\frac {e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+4 \text {$\#$1}-1}\&\right ]+c_2 \text {RootSum}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-5\&,\frac {\text {$\#$1} e^{\text {$\#$1} t}-e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+4 \text {$\#$1}-1}\&\right ]+c_3 \text {RootSum}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-5\&,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}+\text {$\#$1} e^{\text {$\#$1} t}-3 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+4 \text {$\#$1}-1}\&\right ] \end{align*}
✗ Sympy
from sympy import *
t = symbols("t")
x1 = Function("x1")
x2 = Function("x2")
x3 = Function("x3")
ode=[Eq(-x1(t) - x2(t) - x3(t) + Derivative(x1(t), t),0),Eq(-x1(t) + 2*x2(t) + x3(t) + Derivative(x2(t), t),0),Eq(-x2(t) + x3(t) + Derivative(x3(t), t),0)]
ics = {}
dsolve(ode,func=[x1(t),x2(t),x3(t)],ics=ics)
Timed Out