Internal problem ID [11433]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises
page 41
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }+p \left (t \right ) x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(diff(x(t),t)+p(t)*x(t)=0,x(t), singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{\int -p \left (t \right )d t} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 27
DSolve[x'[t]+p[t]*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \exp \left (\int _1^t-p(K[1])dK[1]\right ) x(t)\to 0 \end{align*}