Internal problem ID [5476]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (2+x \right ) \sin \relax (y)+\cos \relax (y) y^{\prime } x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.028 (sec). Leaf size: 16
dsolve((x+2)*sin(y(x))+x*cos(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (\frac {{\mathrm e}^{-x}}{c_{1} x^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 73.618 (sec). Leaf size: 23
DSolve[(x+2)*Sin[y[x]]+x*Cos[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \csc ^{-1}\left (x^2 e^{x-c_1}\right ) \\ y(x)\to 0 \\ \end{align*}