63.5.25 problem 12

Internal problem ID [13099]
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
Date solved : Tuesday, January 28, 2025 at 04:52:16 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }+p \left (t \right ) x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 13

dsolve(diff(x(t),t)+p(t)*x(t)=0,x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 27

DSolve[D[x[t],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*}