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 : Monday, January 27, 2025 at 04:35:10 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 1.170 (sec). Leaf size: 63

DSolve[D[y[x],x] == Cos[x]^2*Cos[2*y[x]]^2,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*}