32.4.2 problem Recognizable Exact Differential equations. Integrating factors. Example 10.52, page 90

Internal problem ID [5813]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number : Recognizable Exact Differential equations. Integrating factors. Example 10.52, page 90
Date solved : Monday, January 27, 2025 at 01:19:54 PM
CAS classification : [_separable]

\begin{align*} y \sec \left (x \right )+\sin \left (x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 8

dsolve((y(x)*sec(x))+sin(x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \cot \left (x \right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 15

DSolve[(y[x]*Sec[x])+Sin[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \cot (x) \\ y(x)\to 0 \\ \end{align*}