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
:
Wednesday, February 05, 2025 at 03:46:07 AM
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*}
✓ Solution by Maple
Time used: 0.400 (sec). Leaf size: 3195
dsolve([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],singsol=all)
\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_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 )+{\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 ) \\
\text {Expression too large to display} \\
\end{align*}
✓ Solution by Mathematica
Time used: 0.170 (sec). Leaf size: 2759
DSolve[{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},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
Too large to display