Internal problem ID [6256]
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. Problems for Review and Discovery. Page
53
Problem number: 1(h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-\sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 11
dsolve(-sin(x)*sin(y(x))+cos(x)*cos(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \arcsin \left (\frac {c_{1}}{\cos \left (x \right )}\right ) \]
✓ Solution by Mathematica
Time used: 3.473 (sec). Leaf size: 19
DSolve[-Sin[x]*Sin[y[x]]+Cos[x]*Cos[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \arcsin \left (\frac {1}{2} c_1 \sec (x)\right ) y(x)\to 0 \end{align*}