Internal problem ID [5995]
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 }\relax (t )&=3 x \relax (t )-y \relax (t )-z \relax (t )\\ y^{\prime }\relax (t )&=x \relax (t )+y \relax (t )-z \relax (t )\\ z^{\prime }\relax (t )&=x \relax (t )-y \relax (t )+z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 57
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)],[x(t), y(t), z(t)], singsol=all)
\[ x \relax (t ) = 2 c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{t}+c_{1} {\mathrm e}^{2 t} \] \[ y \relax (t ) = c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{t}+c_{1} {\mathrm e}^{2 t} \] \[ z \relax (t ) = c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.013 (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*}