Internal problem ID [3083]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 7, page 37
Problem number: 1.d.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x \sin \left (\frac {y}{x}\right ) y^{\prime }-\sin \left (\frac {y}{x}\right ) y=x} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \left (\pi -\arccos \left (\ln \left (x \right )+c_{1} \right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.435 (sec). Leaf size: 34
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 \arccos (-\log (x)-c_1) y(x)\to x \arccos (-\log (x)-c_1) \end{align*}