20.20.33 problem 37

Internal problem ID [3923]
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 : 37
Date solved : Monday, January 27, 2025 at 08:04:35 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 19

dsolve([diff(x__1(t),t)=-4*x__1(t)+0*x__2(t),diff(x__2(t),t)=0*x__1(t)-4*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{-4 t} \\ x_{2} \left (t \right ) &= {\mathrm e}^{-4 t} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 65

DSolve[{D[x1[t],t]==-4*x1[t]+0*x2[t],D[x2[t],t]==0*x1[t]-4*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to c_1 e^{-4 t} \\ \text {x2}(t)\to c_2 e^{-4 t} \\ \text {x1}(t)\to c_1 e^{-4 t} \\ \text {x2}(t)\to 0 \\ \text {x1}(t)\to 0 \\ \text {x2}(t)\to c_2 e^{-4 t} \\ \text {x1}(t)\to 0 \\ \text {x2}(t)\to 0 \\ \end{align*}