50.5.4 problem 1(d)

Internal problem ID [7874]
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 1.7. Homogeneous Equations. Page 28
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 03:29:34 PM
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: 0.005 (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: 0.466 (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*}