Internal problem ID [2585]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 8, page 41
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 31
dsolve(cos(x)*cos(y(x))^2+(2*sin(x)*sin(y(x))*cos(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\pi }{2} \\ y \left (x \right ) = \arccos \left (\sqrt {\sin \left (x \right ) c_{1}}\right ) \\ y \left (x \right ) = \pi -\arccos \left (\sqrt {\sin \left (x \right ) c_{1}}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 6.216 (sec). Leaf size: 85
DSolve[Cos[x]*Cos[y[x]]^2+(2*Sin[x]*Sin[y[x]]*Cos[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ y(x)\to -\arccos \left (-\frac {1}{4} c_1 \sqrt {\cos (x)} \sqrt {\tan (x)}\right ) \\ y(x)\to \arccos \left (-\frac {1}{4} c_1 \sqrt {\cos (x)} \sqrt {\tan (x)}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}