20.20.31 problem 35

Internal problem ID [3921]
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 : 35
Date solved : Monday, January 27, 2025 at 08:04:34 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=-6 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )-5 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 35

dsolve([diff(x__1(t),t)=0*x__1(t)-6*x__2(t),diff(x__2(t),t)=1*x__1(t)-5*x__2(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 59

DSolve[{D[x1[t],t]==0*x1[t]-6*x2[t],D[x2[t],t]==1*x1[t]-5*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to e^{-3 t} \left (c_1 \left (3 e^t-2\right )-6 c_2 \left (e^t-1\right )\right ) \\ \text {x2}(t)\to e^{-3 t} \left (c_1 \left (e^t-1\right )+c_2 \left (3-2 e^t\right )\right ) \\ \end{align*}