58.4.4 problem 4

Internal problem ID [14574]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:42:30 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 9

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

\[ y = \arccos \left (\sin \left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.265 (sec). Leaf size: 27

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

\begin{align*} y(x)&\to -\arccos (\sin (x)-c_1)\\ y(x)&\to \arccos (\sin (x)-c_1) \end{align*}

✓ Sympy. Time used: 0.277 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)/cos(x) + 1/sin(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \operatorname {acos}{\left (C_{1} + \sin {\left (x \right )} \right )} + 2 \pi , \ y{\left (x \right )} = \operatorname {acos}{\left (C_{1} + \sin {\left (x \right )} \right )}\right ] \]