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

Internal problem ID [3961]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {y \sec \relax (x )+y^{\prime } \sin \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 10

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

\[ y \relax (x ) = \frac {c_{1}}{\tan \relax (x )} \]

Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 15

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

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