76.1.5 problem 5

Internal problem ID [17304]
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 : Tuesday, January 28, 2025 at 09:59:11 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 18

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

\[ y = \arctan \left (\frac {x}{2}+4 c_{1} -\frac {\sin \left (4 x \right )}{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.242 (sec). Leaf size: 73

DSolve[D[y[x],x]==Sin[2*x]^2*Cos[y[x]]^2,y[x],x,IncludeSingularSolutions -> True]
 

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