Internal problem ID [5453]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {x \sin \left (\frac {y}{x}\right ) y^{\prime }-y \sin \left (\frac {y}{x}\right )-x=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = \left (\pi -\arccos \left (\ln \relax (x )+c_{1}\right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.35 (sec). Leaf size: 33
DSolve[x*Sin[y[x]/x]*y'[x]==y[x]*Sin[y[x]/x]+x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (-\pi +\text {ArcCos}(\log (x)+c_1)) \\ y(x)\to x (\pi -\text {ArcCos}(\log (x)+c_1)) \\ \end{align*}