23.1.113 problem 116

Internal problem ID [4720]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 116
Date solved : Tuesday, September 30, 2025 at 08:19:43 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\tan \left (x \right ) \sec \left (x \right ) \cos \left (y\right )^{2}&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 11

ode:=diff(y(x),x)+tan(x)*sec(x)*cos(y(x))^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\arctan \left (\sec \left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 1.013 (sec). Leaf size: 31

ode=D[y[x],x]+Tan[x]*Sec[x]*Cos[y[x]]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \arctan (-\sec (x)+c_1)\\ y(x)&\to -\frac {\pi }{2}\\ y(x)&\to \frac {\pi }{2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + cos(y(x))**2*tan(x)/cos(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out