Internal problem ID [5329]
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]
Solve \begin {gather*} \boxed {\cos \relax (x ) \left (\cos ^{2}\relax (y)\right )-\sin \relax (x ) \sin \left (2 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.263 (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 \relax (x ) = \arccos \left (\frac {1}{\sqrt {\sin \relax (x ) c_{1}}}\right ) \\ y \relax (x ) = \pi -\arccos \left (\frac {1}{\sqrt {\sin \relax (x ) c_{1}}}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.511 (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 -\text {ArcCos}\left (-\frac {c_1}{4 \sqrt {\sin (x)}}\right ) \\ y(x)\to \text {ArcCos}\left (-\frac {c_1}{4 \sqrt {\sin (x)}}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}