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 : Tuesday, March 04, 2025 at 11:47:20 PM
CAS classification : [_separable]

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

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

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

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

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

ode=(y[x]*Sec[x])+Sin[x]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.454 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)/cos(x) + sin(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} \cos {\left (x \right )}}{\sqrt {\cos {\left (2 x \right )} - 1}} \]