74.22.5 problem 5

Internal problem ID [16652]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 09:16:15 AM
CAS classification : system_of_ODEs

\begin{align*} x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=1 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 18

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

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