Internal problem ID [6750]
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: 25.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=5 x \left (t \right )-4 y\\ y^{\prime }&=x \left (t \right )+2 z \left (t \right )\\ z^{\prime }\left (t \right )&=2 y+5 z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 63
dsolve([diff(x(t),t)=5*x(t)-4*y(t),diff(y(t),t)=x(t)+2*z(t),diff(z(t),t)=2*y(t)+5*z(t)],singsol=all)
\begin{align*} x \left (t \right ) &= -4 \,{\mathrm e}^{5 t} c_{3} t +{\mathrm e}^{5 t} c_{1} +\frac {4 c_{2}}{5} \\ y \left (t \right ) &= c_{2} +c_{3} {\mathrm e}^{5 t} \\ z \left (t \right ) &= 2 \,{\mathrm e}^{5 t} c_{3} t -\frac {{\mathrm e}^{5 t} c_{1}}{2}+\frac {5 c_{3} {\mathrm e}^{5 t}}{2}-\frac {2 c_{2}}{5} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 141
DSolve[{x'[t]==5*x[t]-4*y[t],y'[t]==x[t]+2*z[t],z'[t]==2*y[t]+5*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{25} \left (c_1 \left (e^{5 t} (29-20 t)-4\right )-4 \left (5 c_2 \left (e^{5 t}-1\right )+2 c_3 \left (e^{5 t} (5 t-1)+1\right )\right )\right ) \\ y(t)\to \frac {1}{5} c_1 \left (e^{5 t}-1\right )+\frac {2}{5} c_3 \left (e^{5 t}-1\right )+c_2 \\ z(t)\to \frac {1}{25} \left (2 c_1 \left (e^{5 t} (5 t-1)+1\right )+10 c_2 \left (e^{5 t}-1\right )+c_3 \left (e^{5 t} (20 t+21)+4\right )\right ) \\ \end{align*}