70.1.5 problem 5

Internal problem ID [18591]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 5
Date solved : Thursday, October 02, 2025 at 03:15:17 PM
CAS classification : [_separable]

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

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

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

\[ y = \arctan \left (\frac {x}{2}+4 c_1 -\frac {\sin \left (4 x \right )}{8}\right ) \]

✓ Mathematica. Time used: 0.157 (sec). Leaf size: 73

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

\[ \text {Solve}\left [-y(x) \int _1^x0dK[1]+\int _1^x(2 \cos (4 K[1])+\cos (4 K[1]-2 y(x))-2 \cos (2 y(x))+\cos (4 K[1]+2 y(x))-2) \sec ^2(y(x))dK[1]+8 \tan (y(x))=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out