20.20.36 problem 40

Internal problem ID [3926]
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 : 40
Date solved : Monday, January 27, 2025 at 08:04:38 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=-2 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )-4 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 30

dsolve([diff(x__1(t),t)=-2*x__1(t)-1*x__2(t),diff(x__2(t),t)=1*x__1(t)-4*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 ) &= {\mathrm e}^{-3 t} \left (c_{2} t +c_{1} -c_{2} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 44

DSolve[{D[x1[t],t]==-2*x1[t]-1*x2[t],D[x2[t],t]==1*x1[t]-4*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to e^{-3 t} (c_1 (t+1)-c_2 t) \\ \text {x2}(t)\to e^{-3 t} ((c_1-c_2) t+c_2) \\ \end{align*}