20.13.4 problem 4

Internal problem ID [3813]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 9, First order linear systems. Section 9.1, page 587
Problem number : 4
Date solved : Monday, January 27, 2025 at 08:02:54 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-4 x_{1} \left (t \right )-6 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 34

dsolve([diff(x__1(t),t)=2*x__1(t)+4*x__2(t),diff(x__2(t),t)=-4*x__1(t)-6*x__2(t)],singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[{D[x1[t],t]==2*x1[t]+4*x2[t],D[x2[t],t]==-4*x1[t]-6*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to e^{-2 t} (4 c_1 t+4 c_2 t+c_1) \\ \text {x2}(t)\to e^{-2 t} (c_2-4 (c_1+c_2) t) \\ \end{align*}