52.9.4 problem 4
Internal
problem
ID
[8382]
Book
:
DIFFERENTIAL
EQUATIONS
with
Boundary
Value
Problems.
DENNIS
G.
ZILL,
WARREN
S.
WRIGHT,
MICHAEL
R.
CULLEN.
Brooks/Cole.
Boston,
MA.
2013.
8th
edition.
Section
:
CHAPTER
8
SYSTEMS
OF
LINEAR
FIRST-ORDER
DIFFERENTIAL
EQUATIONS.
EXERCISES
8.1.
Page
332
Problem
number
:
4
Date
solved
:
Sunday, March 30, 2025 at 12:53:41 PM
CAS
classification
:
system_of_ODEs
\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right )-y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )+2 z \left (t \right )\\ \frac {d}{d t}z \left (t \right )&=-x \left (t \right )+z \left (t \right ) \end{align*}
✓ Maple. Time used: 0.468 (sec). Leaf size: 2265
ode:=[diff(x(t),t) = x(t)-y(t), diff(y(t),t) = x(t)+2*z(t), diff(z(t),t) = -x(t)+z(t)];
dsolve(ode);
\begin{align*} \text {Solution too large to show}\end{align*}
✓ Mathematica. Time used: 0.02 (sec). Leaf size: 503
ode={D[x[t],t]==x[t]-y[t],D[y[t],t]==x[t]+2*z[t],D[z[t],t]==-x[t]+z[t]};
ic={};
DSolve[{ode,ic},{x[t],y[t],z[t]},t,IncludeSingularSolutions->True]
\begin{align*}
x(t)\to -2 c_3 \text {RootSum}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}-3\&,\frac {e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-4 \text {$\#$1}+2}\&\right ]-c_2 \text {RootSum}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}-3\&,\frac {\text {$\#$1} e^{\text {$\#$1} t}-e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-4 \text {$\#$1}+2}\&\right ]+c_1 \text {RootSum}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}-3\&,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}-\text {$\#$1} e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-4 \text {$\#$1}+2}\&\right ] \\
y(t)\to c_1 \text {RootSum}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}-3\&,\frac {\text {$\#$1} e^{\text {$\#$1} t}-3 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-4 \text {$\#$1}+2}\&\right ]+2 c_3 \text {RootSum}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}-3\&,\frac {\text {$\#$1} e^{\text {$\#$1} t}-e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-4 \text {$\#$1}+2}\&\right ]+c_2 \text {RootSum}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}-3\&,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}-2 \text {$\#$1} e^{\text {$\#$1} t}+e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-4 \text {$\#$1}+2}\&\right ] \\
z(t)\to c_2 \text {RootSum}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}-3\&,\frac {e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-4 \text {$\#$1}+2}\&\right ]-c_1 \text {RootSum}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}-3\&,\frac {\text {$\#$1} e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-4 \text {$\#$1}+2}\&\right ]+c_3 \text {RootSum}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}-3\&,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}-\text {$\#$1} e^{\text {$\#$1} t}+e^{\text {$\#$1} t}}{3 \text {$\#$1}^2-4 \text {$\#$1}+2}\&\right ] \\
\end{align*}
✗ Sympy
from sympy import *
t = symbols("t")
x = Function("x")
y = Function("y")
z = Function("z")
ode=[Eq(-x(t) + y(t) + Derivative(x(t), t),0),Eq(-x(t) - 2*z(t) + Derivative(y(t), t),0),Eq(x(t) - z(t) + Derivative(z(t), t),0)]
ics = {}
dsolve(ode,func=[x(t),y(t),z(t)],ics=ics)
Timed Out