10.2.5 problem 5

Internal problem ID [1133]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 5
Date solved : Thursday, March 13, 2025 at 03:53:39 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

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

\[ y = \frac {\arctan \left (x +2 c_1 +\frac {\sin \left (2 x \right )}{2}\right )}{2} \]

✓ Mathematica. Time used: 1.17 (sec). Leaf size: 63

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

\begin{align*} y(x)\to \frac {1}{2} \arctan \left (x+\sin (x) \cos (x)+\frac {c_1}{4}\right ) \\ y(x)\to \frac {1}{2} \arctan \left (x+\sin (x) \cos (x)+\frac {c_1}{4}\right ) \\ y(x)\to -\frac {\pi }{4} \\ y(x)\to \frac {\pi }{4} \\ \end{align*}

✗ Sympy

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

Timed Out