86.1.4 problem 4

Internal problem ID [23066]
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 3b at page 43
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:18:35 PM
CAS classification : [_separable]

\begin{align*} y^{\prime } \sin \left (y\right )&=\sec \left (x \right )^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

ode:=sin(y(x))*diff(y(x),x) = sec(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \pi -\arccos \left (\tan \left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.789 (sec). Leaf size: 31

ode=Sin[y[x]]*D[y[x],x]==Sec[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.375 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sin(y(x))*Derivative(y(x), x) - sec(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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