Internal problem ID [6751]
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: 26.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )\\ y^{\prime }&=3 y+z \left (t \right )\\ z^{\prime }\left (t \right )&=-y+z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 39
dsolve([diff(x(t),t)=x(t),diff(y(t),t)=3*y(t)+z(t),diff(z(t),t)=-y(t)+z(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{3} {\mathrm e}^{t} \\ y \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{2} t +c_{1} \right ) \\ z \left (t \right ) &= -{\mathrm e}^{2 t} \left (c_{2} t +c_{1} -c_{2} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 96
DSolve[{x'[t]==x[t],y'[t]==3*y[t]+z[t],z'[t]==-y[t]+z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^t \\ y(t)\to e^{2 t} (c_2 (t+1)+c_3 t) \\ z(t)\to e^{2 t} (c_3-(c_2+c_3) t) \\ x(t)\to 0 \\ y(t)\to e^{2 t} (c_2 (t+1)+c_3 t) \\ z(t)\to e^{2 t} (c_3-(c_2+c_3) t) \\ \end{align*}