Internal problem ID [5503]
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]
Solve \begin {gather*} \boxed {-\sin \relax (x ) \sin \relax (y)+\cos \relax (x ) \cos \relax (y) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.17 (sec). Leaf size: 11
dsolve(-sin(x)*sin(y(x))+cos(x)*cos(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (\frac {c_{1}}{\cos \relax (x )}\right ) \]
✓ Solution by Mathematica
Time used: 1.272 (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 \text {ArcSin}\left (\frac {1}{2} c_1 \sec (x)\right ) \\ y(x)\to 0 \\ \end{align*}