23.1.121 problem 124

Internal problem ID [4728]
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 : 124
Date solved : Tuesday, September 30, 2025 at 08:20:06 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 22

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

\[ y = \frac {\operatorname {RootOf}\left (-\textit {\_Z} +4 c_1 +4 \sin \left (x \right )-\sin \left (\textit {\_Z} \right )\right )}{2} \]

✓ Mathematica. Time used: 0.17 (sec). Leaf size: 37

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

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}(\cos (2 K[1])+1)dK[1]\&\right ]\left [\int _1^x2 \cos (K[2])dK[2]+c_1\right ] \end{align*}

✓ Sympy. Time used: 2.980 (sec). Leaf size: 20

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

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