65.3.6 problem 8.2

Internal problem ID [13724]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 8, Separable equations. Exercises page 72
Problem number : 8.2
Date solved : Tuesday, January 28, 2025 at 05:59:49 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }+p x&=q \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

dsolve(diff(x(t),t)+p*x(t)=q,x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 29

DSolve[D[x[t],t]+p*x[t]==q,x[t],t,IncludeSingularSolutions -> True]
 

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