Internal problem ID [6752]
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: 27.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )\\ y^{\prime }&=2 x \left (t \right )+2 y-z \left (t \right )\\ z^{\prime }\left (t \right )&=y \end {align*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 46
dsolve([diff(x(t),t)=x(t),diff(y(t),t)=2*x(t)+2*y(t)-z(t),diff(z(t),t)=y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{3} {\mathrm e}^{t} \\ y \left (t \right ) &= {\mathrm e}^{t} \left (c_{3} t^{2}+c_{1} t +2 c_{3} t +c_{1} +c_{2} \right ) \\ z \left (t \right ) &= {\mathrm e}^{t} \left (c_{3} t^{2}+c_{1} t +c_{2} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 65
DSolve[{x'[t]==x[t],y'[t]==2*x[t]+2*y[t]-z[t],z'[t]==y[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^t \\ y(t)\to e^t \left (c_1 t^2+(2 c_1+c_2-c_3) t+c_2\right ) \\ z(t)\to e^t \left (c_1 t^2+(c_2-c_3) t+c_3\right ) \\ \end{align*}