50.8.8 problem 1(h)

Internal problem ID [7924]
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)
Date solved : Monday, January 27, 2025 at 03:32:35 PM
CAS classification : [_separable]

\begin{align*} -\sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.088 (sec). Leaf size: 9

dsolve(-sin(x)*sin(y(x))+cos(x)*cos(y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \arcsin \left (\sec \left (x \right ) c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 3.362 (sec). Leaf size: 19

DSolve[-Sin[x]*Sin[y[x]]+Cos[x]*Cos[y[x]]*D[y[x],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*}