Internal problem ID [5434]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page
20
Problem number: 6.
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 )+2 \sin \relax (x ) \cos \relax (y) y^{\prime } \sin \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.239 (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 \relax (x ) = \frac {\pi }{2} \\ y \relax (x ) = \arccos \left (\sqrt {\sin \relax (x ) c_{1}}\right ) \\ y \relax (x ) = \pi -\arccos \left (\sqrt {\sin \relax (x ) c_{1}}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.985 (sec). Leaf size: 73
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 -\text {ArcCos}\left (-\frac {1}{4} c_1 \sqrt {\sin (x)}\right ) \\ y(x)\to \text {ArcCos}\left (-\frac {1}{4} c_1 \sqrt {\sin (x)}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}