Internal problem ID [2856]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 107.
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 ) \cos \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.265 (sec). Leaf size: 69
dsolve(diff(y(x),x) = cos(x)^2*cos(y(x)),y(x), singsol=all)
\[ y \relax (x ) = \arctan \left (\frac {c_{1}^{2} {\mathrm e}^{x +\frac {\sin \left (2 x \right )}{2}}-1}{c_{1}^{2} {\mathrm e}^{x +\frac {\sin \left (2 x \right )}{2}}+1}, \frac {2 c_{1} {\mathrm e}^{\frac {x}{2}+\frac {\sin \left (2 x \right )}{4}}}{c_{1}^{2} {\mathrm e}^{x +\frac {\sin \left (2 x \right )}{2}}+1}\right ) \]
✓ Solution by Mathematica
Time used: 1.007 (sec). Leaf size: 41
DSolve[y'[x]==Cos[x]^2 Cos[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \text {ArcTan}\left (\tanh \left (\frac {1}{8} (2 x+\sin (2 x)+c_1)\right )\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}