Internal problem ID [6753]
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: 28.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 x \left (t \right )+y\\ y^{\prime }&=4 y+z \left (t \right )\\ z^{\prime }\left (t \right )&=4 z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 46
dsolve([diff(x(t),t)=4*x(t)+y(t),diff(y(t),t)=4*y(t)+z(t),diff(z(t),t)=4*z(t)],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {\left (c_{3} t^{2}+2 c_{2} t +2 c_{1} \right ) {\mathrm e}^{4 t}}{2} \\ y \left (t \right ) &= \left (c_{3} t +c_{2} \right ) {\mathrm e}^{4 t} \\ z \left (t \right ) &= c_{3} {\mathrm e}^{4 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 57
DSolve[{x'[t]==4*x[t]+y[t],y'[t]==4*y[t]+z[t],z'[t]==4*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{4 t} (t (c_3 t+2 c_2)+2 c_1) \\ y(t)\to e^{4 t} (c_3 t+c_2) \\ z(t)\to c_3 e^{4 t} \\ \end{align*}