Internal problem ID [14923]
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: 6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+1\\ x_{2}^{\prime }\left (t \right )&=x_{2} \left (t \right ) \end {align*}
With initial conditions \[ [x_{1} \left (0\right ) = 0, x_{2} \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(x__1(t),t) = -x__1(t)+1, diff(x__2(t),t) = x__2(t), x__1(0) = 0, x__2(0) = 1], singsol=all)
\begin{align*} x_{1} \left (t \right ) &= 1-{\mathrm e}^{-t} \\ x_{2} \left (t \right ) &= {\mathrm e}^{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 12
DSolve[{x1'[t]==-x1[t],x2'[t]==x2[t]},{x1[0]==0,x2[0]==1},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to 0 \\ \text {x2}(t)\to e^t \\ \end{align*}