Internal problem ID [12817]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Exercises section 3.8 page 371
Problem number: 14.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )+y\\ y^{\prime }&=-2 y+z \left (t \right )\\ z^{\prime }\left (t \right )&=-2 z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 46
dsolve([diff(x(t),t)=-2*x(t)+1*y(t)+0*z(t),diff(y(t),t)=0*x(t)-2*y(t)+1*z(t),diff(z(t),t)=0*x(t)+0*y(t)-2*z(t)],[x(t), y(t), z(t)], singsol=all)
\begin{align*} x \left (t \right ) = \frac {\left (c_{3} t^{2}+2 c_{2} t +2 c_{1} \right ) {\mathrm e}^{-2 t}}{2} y \left (t \right ) = \left (c_{3} t +c_{2} \right ) {\mathrm e}^{-2 t} z \left (t \right ) = c_{3} {\mathrm e}^{-2 t} \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 57
DSolve[{x'[t]==-2*x[t]+1*y[t]+0*z[t],y'[t]==0*x[t]-2*y[t]+1*z[t],z'[t]==0*x[t]+0*y[t]-2*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{-2 t} (t (c_3 t+2 c_2)+2 c_1) y(t)\to e^{-2 t} (c_3 t+c_2) z(t)\to c_3 e^{-2 t} \end{align*}