20.15.6 problem 6

Internal problem ID [3832]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 9, First order linear systems. Section 9.3, page 598
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 02:39:18 PM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 14

dsolve([diff(x__1(t),t)=1/t*x__1(t),diff(x__2(t),t)=x__2(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 53

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

\begin{align*} \text {x1}(t)\to c_1 t \\ \text {x2}(t)\to c_2 e^t \\ \text {x1}(t)\to c_1 t \\ \text {x2}(t)\to 0 \\ \text {x1}(t)\to 0 \\ \text {x2}(t)\to c_2 e^t \\ \text {x1}(t)\to 0 \\ \text {x2}(t)\to 0 \\ \end{align*}