20.20.4 problem 4

Internal problem ID [3894]
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 : 4
Date solved : Monday, January 27, 2025 at 08:04:09 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=9 x_{1} \left (t \right )-2 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: 0.029 (sec). Leaf size: 35

dsolve([diff(x__1(t),t)=9*x__1(t)-2*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 ) &= c_{1} {\mathrm e}^{8 t}+c_{2} {\mathrm e}^{-t} \\ x_{2} \left (t \right ) &= \frac {c_{1} {\mathrm e}^{8 t}}{2}+5 c_{2} {\mathrm e}^{-t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 73

DSolve[{D[x1[t],t]==9*x1[t]-2*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 \frac {1}{9} e^{-t} \left (c_1 \left (10 e^{9 t}-1\right )-2 c_2 \left (e^{9 t}-1\right )\right ) \\ \text {x2}(t)\to \frac {1}{9} e^{-t} \left (5 c_1 \left (e^{9 t}-1\right )-c_2 \left (e^{9 t}-10\right )\right ) \\ \end{align*}