20.20.3 problem 3

Internal problem ID [3893]
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 : 3
Date solved : Monday, January 27, 2025 at 08:04:08 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=-6 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=6 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 35

dsolve([diff(x__1(t),t)=-6*x__1(t)+x__2(t),diff(x__2(t),t)=6*x__1(t)-5*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-8 t} c_{1} +c_{2} {\mathrm e}^{-3 t} \\ x_{2} \left (t \right ) &= -2 \,{\mathrm e}^{-8 t} c_{1} +3 c_{2} {\mathrm e}^{-3 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 73

DSolve[{D[x1[t],t]==-6*x1[t]+x2[t],D[x2[t],t]==6*x1[t]-5*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to \frac {1}{5} e^{-8 t} \left (c_1 \left (2 e^{5 t}+3\right )+c_2 \left (e^{5 t}-1\right )\right ) \\ \text {x2}(t)\to \frac {1}{5} e^{-8 t} \left (6 c_1 \left (e^{5 t}-1\right )+c_2 \left (3 e^{5 t}+2\right )\right ) \\ \end{align*}