23.1.108 problem 109

Internal problem ID [4715]
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 : 109
Date solved : Tuesday, September 30, 2025 at 08:19:16 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.052 (sec). Leaf size: 69

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

\[ y = \arctan \left (\frac {c_1^{2} {\mathrm e}^{x +\frac {\sin \left (2 x \right )}{2}}-1}{c_1^{2} {\mathrm e}^{x +\frac {\sin \left (2 x \right )}{2}}+1}, \frac {2 c_1 \,{\mathrm e}^{\frac {x}{2}+\frac {\sin \left (2 x \right )}{4}}}{c_1^{2} {\mathrm e}^{x +\frac {\sin \left (2 x \right )}{2}}+1}\right ) \]

✓ Mathematica. Time used: 0.081 (sec). Leaf size: 61

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

\[ \text {Solve}\left [-y(x) \int _1^x0dK[1]+\int _1^x-((\cos (2 K[1]-y(x))+2 \cos (y(x))+\cos (2 K[1]+y(x))) \sec (y(x)))dK[1]+4 \coth ^{-1}(\sin (y(x)))=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out