76.4.18 problem 22

Internal problem ID [17412]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 10:06:20 AM
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: 0.081 (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: 46.669 (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*}