29.4.18 problem 107

Internal problem ID [4709]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 107
Date solved : Sunday, March 30, 2025 at 03:46:42 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: 1.018 (sec). Leaf size: 41

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

\begin{align*} y(x)\to 2 \arctan \left (\tanh \left (\frac {1}{8} (2 x+\sin (2 x)+c_1)\right )\right ) \\ 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(-cos(x)**2*cos(y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out