20.19.5 problem 6

Internal problem ID [3885]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 9, First order linear systems. Section 9.8 (Matrix exponential function), page 642
Problem number : 6
Date solved : Monday, January 27, 2025 at 08:03:53 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 42

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

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