Internal problem ID [6082]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 5. Existence and uniqueness of solutions to first order equations. Page
198
Problem number: 1(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\cos \left (x \right ) \cos \left (y\right )^{2}-\sin \left (x \right ) \sin \left (2 y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 25
dsolve(cos(x)*cos(y(x))^2-sin(x)*sin(2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \arccos \left (\frac {1}{\sqrt {c_{1} \sin \left (x \right )}}\right ) y \left (x \right ) = \pi -\arccos \left (\frac {1}{\sqrt {c_{1} \sin \left (x \right )}}\right ) \end{align*}
✓ Solution by Mathematica
Time used: 6.536 (sec). Leaf size: 73
DSolve[Cos[x]*Cos[y[x]]^2-Sin[x]*Sin[2*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 {c_1}{4 \sqrt {\sin (x)}}\right ) y(x)\to \arccos \left (-\frac {c_1}{4 \sqrt {\sin (x)}}\right ) y(x)\to -\frac {\pi }{2} y(x)\to \frac {\pi }{2} \end{align*}