50.6.5 problem 1(e)

Internal problem ID [7897]
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 1.8. Integrating Factors. Page 32
Problem number : 1(e)
Date solved : Monday, January 27, 2025 at 03:31:36 PM
CAS classification : [_separable]

\begin{align*} \left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 16

dsolve((x+2)*sin(y(x))+x*cos(y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \arcsin \left (\frac {{\mathrm e}^{-x}}{c_{1} x^{2}}\right ) \]

✓ Solution by Mathematica

Time used: 46.612 (sec). Leaf size: 24

DSolve[(x+2)*Sin[y[x]]+x*Cos[y[x]]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \arcsin \left (\frac {e^{-x-2+c_1}}{x^2}\right ) \\ y(x)\to 0 \\ \end{align*}