20.13.11 problem 11

Internal problem ID [3820]
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 : 11
Date solved : Monday, January 27, 2025 at 08:03:00 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*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) = 1\\ x_{2} \left (0\right ) = 3 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 27

dsolve([diff(x__1(t),t) = 2*x__1(t)+x__2(t), diff(x__2(t),t) = -x__1(t)+4*x__2(t), x__1(0) = 1, x__2(0) = 3], singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{3 t} \left (1+2 t \right ) \\ x_{2} \left (t \right ) &= {\mathrm e}^{3 t} \left (2 t +3\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[{D[x1[t],t]==2*x1[t]+x2[t],D[x2[t],t]==-x1[t]+4*x2[t]},{x1[0]==1,x2[0]==3},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to e^{3 t} (2 t+1) \\ \text {x2}(t)\to e^{3 t} (2 t+3) \\ \end{align*}