65.2.1 problem 7.1 (i)

Internal problem ID [13714]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 7, Scalar autonomous ODEs. Exercises page 56
Problem number : 7.1 (i)
Date solved : Tuesday, January 28, 2025 at 05:55:51 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=-x+1 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 12

dsolve(diff(x(t),t)=-x(t)+1,x(t), singsol=all)
 

\[ x \left (t \right ) = 1+{\mathrm e}^{-t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 20

DSolve[D[x[t],t]==-x[t]+1,x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to 1+c_1 e^{-t} \\ x(t)\to 1 \\ \end{align*}