20.20.30 problem 34

Internal problem ID [3920]
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 : 34
Date solved : Monday, January 27, 2025 at 08:04:33 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=8 x_{1} \left (t \right )+x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 35

dsolve([diff(x__1(t),t)=-3*x__1(t)+4*x__2(t),diff(x__2(t),t)=8*x__1(t)+1*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{-7 t}+c_{2} {\mathrm e}^{5 t} \\ x_{2} \left (t \right ) &= -c_{1} {\mathrm e}^{-7 t}+2 c_{2} {\mathrm e}^{5 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 71

DSolve[{D[x1[t],t]==-3*x1[t]+4*x2[t],D[x2[t],t]==8*x1[t]+1*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to \frac {1}{3} e^{-7 t} \left (c_1 \left (e^{12 t}+2\right )+c_2 \left (e^{12 t}-1\right )\right ) \\ \text {x2}(t)\to \frac {1}{3} e^{-7 t} \left (2 c_1 \left (e^{12 t}-1\right )+c_2 \left (2 e^{12 t}+1\right )\right ) \\ \end{align*}