78.3.4 problem 1 (d)

Internal problem ID [18107]
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 7 (Homogeneous Equations). Problems at page 67
Problem number : 1 (d)
Date solved : Tuesday, January 28, 2025 at 11:27:53 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

dsolve(x*sin(y(x)/x)*diff(y(x),x)=y(x)*sin(y(x)/x)+x,y(x), singsol=all)
 

\[ y = \left (\frac {\pi }{2}+\arcsin \left (\ln \left (x \right )+c_1 \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.406 (sec). Leaf size: 34

DSolve[x*Sin[y[x]/x]*D[y[x],x]==y[x]*Sin[y[x]/x]+x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x \arccos (-\log (x)-c_1) \\ y(x)\to x \arccos (-\log (x)-c_1) \\ \end{align*}