Internal problem ID [483]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\left (\cos ^{2}\relax (x )\right ) \left (\cos ^{2}\left (2 y\right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x) = cos(x)^2*cos(2*y(x))^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\arctan \left (x +2 c_{1}+\frac {\sin \left (2 x \right )}{2}\right )}{2} \]
✓ Solution by Mathematica
Time used: 1.32 (sec). Leaf size: 63
DSolve[y'[x] == Cos[x]^2*Cos[2*y[x]]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \text {ArcTan}\left (x+\sin (x) \cos (x)+\frac {c_1}{4}\right ) \\ y(x)\to \frac {1}{2} \text {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*}