20.13.10 problem 10

Internal problem ID [3819]
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 : 10
Date solved : Monday, January 27, 2025 at 08:02:59 AM
CAS classification : system_of_ODEs

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) = 0\\ x_{2} \left (0\right ) = 1 \end{align*}

Solution by Maple

Time used: 0.024 (sec). Leaf size: 18

dsolve([diff(x__1(t),t) = 2*x__1(t)+5*x__2(t), diff(x__2(t),t) = -x__1(t)-2*x__2(t), x__1(0) = 0, x__2(0) = 1], singsol=all)
 
\begin{align*} x_{1} \left (t \right ) &= 5 \sin \left (t \right ) \\ x_{2} \left (t \right ) &= \cos \left (t \right )-2 \sin \left (t \right ) \\ \end{align*}

Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 19

DSolve[{D[x1[t],t]==2*x1[t]+5*x2[t],D[x2[t],t]==-x1[t]-2*x2[t]},{x1[0]==0,x2[0]==1},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 
\begin{align*} \text {x1}(t)\to 5 \sin (t) \\ \text {x2}(t)\to \cos (t)-2 \sin (t) \\ \end{align*}