Internal problem ID [11019]
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 }\left (t \right )&=y \left (t \right )-x \left (t \right )\\ z^{\prime }\left (t \right )&=-x \left (t \right )-2 y \left (t \right )+3 z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 49
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],[x(t), y(t), z(t)], singsol=all)
\[ x \left (t \right ) = \frac {c_{3} {\mathrm e}^{3 t}}{4}-c_{2} +c_{1} +c_{2} t \] \[ y \left (t \right ) = -\frac {c_{3} {\mathrm e}^{3 t}}{8}+c_{1} +c_{2} t \] \[ z \left (t \right ) = c_{1} +c_{2} t +c_{3} {\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 126
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)-2 (c_2-c_3) \left (e^{3 t}-1\right )+3 (2 c_2+c_3) t\right ) \\ y(t)\to \frac {1}{9} \left ((c_2-c_3) e^{3 t}+3 (-3 c_1+2 c_2+c_3) t+8 c_2+c_3\right ) \\ z(t)\to \frac {1}{9} \left (-8 (c_2-c_3) e^{3 t}+3 (-3 c_1+2 c_2+c_3) t+8 c_2+c_3\right ) \\ \end{align*}