78.5.5 problem 2 (e)

Internal problem ID [18148]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 9 (Integrating Factors). Problems at page 80
Problem number : 2 (e)
Date solved : Tuesday, January 28, 2025 at 11:34:06 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: 0.010 (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: 46.327 (sec). Leaf size: 23

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+c_1}}{x^2}\right ) \\ y(x)\to 0 \\ \end{align*}