Internal problem ID [12822]
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: 20.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-y+z \left (t \right )\\ y^{\prime }&=-x \left (t \right )+z \left (t \right )\\ z^{\prime }\left (t \right )&=z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
dsolve([diff(x(t),t)=-y(t)+z(t),diff(y(t),t)=-x(t)+z(t),diff(z(t),t)=z(t)],[x(t), y(t), z(t)], singsol=all)
\begin{align*} x \left (t \right ) = -c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{t} y \left (t \right ) = c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-t} z \left (t \right ) = c_{3} {\mathrm e}^{t} \end{align*}
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 94
DSolve[{x'[t]==-y[t]+z[t],y'[t]==-x[t]+z[t],z'[t]==z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{-t} \left (c_1 \left (e^{2 t}+1\right )-(c_2-c_3) \left (e^{2 t}-1\right )\right ) y(t)\to \frac {1}{2} e^{-t} \left (-\left (c_1 \left (e^{2 t}-1\right )\right )+c_2 \left (e^{2 t}+1\right )+c_3 \left (e^{2 t}-1\right )\right ) z(t)\to c_3 e^t \end{align*}