Internal problem ID [6748]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.
EXERCISES 8.2. Page 346
Problem number: 23.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )-y-z \left (t \right )\\ y^{\prime }&=x \left (t \right )+y-z \left (t \right )\\ z^{\prime }\left (t \right )&=x \left (t \right )-y+z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 51
dsolve([diff(x(t),t)=3*x(t)-y(t)-z(t),diff(y(t),t)=x(t)+y(t)-z(t),diff(z(t),t)=x(t)-y(t)+z(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{t}+c_{3} {\mathrm e}^{2 t} \\ y \left (t \right ) &= c_{2} {\mathrm e}^{t}+c_{3} {\mathrm e}^{2 t}+c_{1} {\mathrm e}^{2 t} \\ z \left (t \right ) &= c_{2} {\mathrm e}^{t}-c_{1} {\mathrm e}^{2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 86
DSolve[{x'[t]==3*x[t]-y[t]-z[t],y'[t]==x[t]+y[t]-z[t],z'[t]==x[t]-y[t]+z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t \left (c_1 \left (2 e^t-1\right )-(c_2+c_3) \left (e^t-1\right )\right ) \\ y(t)\to e^t \left (c_1 \left (e^t-1\right )-c_3 e^t+c_2+c_3\right ) \\ z(t)\to e^t \left (c_1 \left (e^t-1\right )-c_2 e^t+c_2+c_3\right ) \\ \end{align*}