Internal problem ID [14922]
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.
ODE order: 1.
ODE degree: 1.
Solve \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 \[ [x_{1} \left (0\right ) = -1, x_{2} \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 17
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: 0.045 (sec). Leaf size: 18
DSolve[{x1'[t]==-3*x1[t],x2'[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*}