86.2.6 problem 6

Internal problem ID [23080]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 3. Some standard types of differential equations. Exercise 3c at page 50
Problem number : 6
Date solved : Thursday, October 02, 2025 at 09:19:14 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\sin \left (x \right ) \sin \left (y\right )}{\cos \left (x \right ) \cos \left (y\right )} \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 9

ode:=diff(y(x),x) = sin(x)*sin(y(x))/cos(x)/cos(y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arcsin \left (c_1 \sec \left (x \right )\right ) \]

✓ Mathematica. Time used: 2.705 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to \arcsin \left (\frac {1}{2} c_1 \sec (x)\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.351 (sec). Leaf size: 19

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

\[ \left [ y{\left (x \right )} = \pi - \operatorname {asin}{\left (\frac {C_{1}}{\cos {\left (x \right )}} \right )}, \ y{\left (x \right )} = \operatorname {asin}{\left (\frac {C_{1}}{\cos {\left (x \right )}} \right )}\right ] \]