20.20.6 problem 6

Internal problem ID [3896]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 9, First order linear systems. Section 9.11 (Chapter review), page 665
Problem number : 6
Date solved : Monday, January 27, 2025 at 08:04:11 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=-8 x_{1} \left (t \right )+5 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-5 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 32

dsolve([diff(x__1(t),t)=-8*x__1(t)+5*x__2(t),diff(x__2(t),t)=-5*x__1(t)+2*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-3 t} \left (c_{2} t +c_{1} \right ) \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{-3 t} \left (5 c_{2} t +5 c_{1} +c_{2} \right )}{5} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 46

DSolve[{D[x1[t],t]==-8*x1[t]+5*x2[t],D[x2[t],t]==-5*x1[t]+2*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to e^{-3 t} (-5 c_1 t+5 c_2 t+c_1) \\ \text {x2}(t)\to e^{-3 t} (-5 c_1 t+5 c_2 t+c_2) \\ \end{align*}