7.24.7 problem 17
Internal
problem
ID
[607]
Book
:
Elementary
Differential
Equations.
By
C.
Henry
Edwards,
David
E.
Penney
and
David
Calvis.
6th
edition.
2008
Section
:
Chapter
5.
Linear
systems
of
differential
equations.
Section
5.3
(Matrices
and
linear
systems).
Problems
at
page
364
Problem
number
:
17
Date
solved
:
Saturday, March 29, 2025 at 04:59:26 PM
CAS
classification
:
system_of_ODEs
\begin{align*} \frac {d}{d t}x \left (t \right )&=3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+t\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )-3 z \left (t \right )+t^{2}\\ \frac {d}{d t}z \left (t \right )&=6 y \left (t \right )-7 z \left (t \right )+t^{3} \end{align*}
✓ Maple. Time used: 0.605 (sec). Leaf size: 3195
ode:=[diff(x(t),t) = 3*x(t)-4*y(t)+z(t)+t, diff(y(t),t) = x(t)-3*z(t)+t^2, diff(z(t),t) = 6*y(t)-7*z(t)+t^3];
dsolve(ode);
\begin{align*}
\text {Expression too large to display} \\
y \left (t \right ) &= -\frac {5 t^{3}}{16}+\frac {465 t^{2}}{512}-\frac {5295 t}{8192}+\frac {14289}{262144}+c_1 \,{\mathrm e}^{-\frac {\left (3 \sqrt {16311}\, \left (386+3 \sqrt {16311}\right )^{{2}/{3}}-386 \left (386+3 \sqrt {16311}\right )^{{2}/{3}}-169 \left (386+3 \sqrt {16311}\right )^{{1}/{3}}+676\right ) t}{507}}+{\mathrm e}^{\frac {\left (3 \sqrt {16311}\, \left (386+3 \sqrt {16311}\right )^{{2}/{3}}-386 \left (386+3 \sqrt {16311}\right )^{{2}/{3}}-169 \left (386+3 \sqrt {16311}\right )^{{1}/{3}}-1352\right ) t}{1014}} c_2 \cos \left (\frac {\left (386+3 \sqrt {16311}\right )^{{1}/{3}} \left (386 \sqrt {3}\, \left (386+3 \sqrt {16311}\right )^{{1}/{3}}-9 \sqrt {5437}\, \left (386+3 \sqrt {16311}\right )^{{1}/{3}}-169 \sqrt {3}\right ) t}{1014}\right )+{\mathrm e}^{\frac {\left (3 \sqrt {16311}\, \left (386+3 \sqrt {16311}\right )^{{2}/{3}}-386 \left (386+3 \sqrt {16311}\right )^{{2}/{3}}-169 \left (386+3 \sqrt {16311}\right )^{{1}/{3}}-1352\right ) t}{1014}} c_3 \sin \left (\frac {\left (386+3 \sqrt {16311}\right )^{{1}/{3}} \left (386 \sqrt {3}\, \left (386+3 \sqrt {16311}\right )^{{1}/{3}}-9 \sqrt {5437}\, \left (386+3 \sqrt {16311}\right )^{{1}/{3}}-169 \sqrt {3}\right ) t}{1014}\right ) \\
\text {Expression too large to display} \\
\end{align*}
✓ Mathematica. Time used: 0.17 (sec). Leaf size: 2759
ode={D[x[t],t]==3*x[t]-4*y[t]+z[t]+t,D[y[t],t]==x[t]-3*z[t]+t^2,D[z[t],t]==6*y[t]-7*z[t]+t^3};
ic={};
DSolve[{ode,ic},{x[t],y[t],z[t]},t,IncludeSingularSolutions->True]
Too large to display
✗ Sympy
from sympy import *
t = symbols("t")
x = Function("x")
y = Function("y")
z = Function("z")
ode=[Eq(-t - 3*x(t) + 4*y(t) - z(t) + Derivative(x(t), t),0),Eq(-t**2 - x(t) + 3*z(t) + Derivative(y(t), t),0),Eq(-t**3 - 6*y(t) + 7*z(t) + Derivative(z(t), t),0)]
ics = {}
dsolve(ode,func=[x(t),y(t),z(t)],ics=ics)
Timed Out