Internal problem ID [12367]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A.
Dobrushkin. CRC Press 2015
Section: Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number: Problem 3(f).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )+z \left (t \right )\\ y^{\prime }&=-x \left (t \right )+y\\ z^{\prime }\left (t \right )&=-x \left (t \right )-2 y+3 z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 48
dsolve([diff(x(t),t)+x(t)-z(t)=0,diff(y(t),t)-y(t)+x(t)=0,diff(z(t),t)+x(t)+2*y(t)-3*z(t)=0],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} +c_{2} t +c_{3} {\mathrm e}^{3 t} \\ y \left (t \right ) &= -\frac {c_{3} {\mathrm e}^{3 t}}{2}+c_{2} +c_{1} +c_{2} t \\ z \left (t \right ) &= c_{2} +4 c_{3} {\mathrm e}^{3 t}+c_{1} +c_{2} t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 132
DSolve[{x'[t]+x[t]-z[t]==0,y'[t]-y[t]+x[t]==0,z'[t]+x[t]+2*y[t]-3*z[t]==0},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{9} \left (-9 c_1 (t-1)+c_2 \left (6 t-2 e^{3 t}+2\right )+c_3 \left (3 t+2 e^{3 t}-2\right )\right ) \\ y(t)\to \frac {1}{9} \left (-9 c_1 t+c_2 \left (6 t+e^{3 t}+8\right )+c_3 \left (3 t-e^{3 t}+1\right )\right ) \\ z(t)\to \frac {1}{9} \left (-9 c_1 t-2 c_2 \left (-3 t+4 e^{3 t}-4\right )+c_3 \left (3 t+8 e^{3 t}+1\right )\right ) \\ \end{align*}