Internal problem ID [7703]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 123.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {x y^{\prime }-x \sin \left (\frac {y}{x}\right )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.036 (sec). Leaf size: 44
dsolve(x*diff(y(x),x) - x*sin(y(x)/x) - y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \arctan \left (\frac {2 x c_{1}}{c_{1}^{2} x^{2}+1}, -\frac {c_{1}^{2} x^{2}-1}{c_{1}^{2} x^{2}+1}\right ) x \]
✓ Solution by Mathematica
Time used: 2.266 (sec). Leaf size: 41
DSolve[x*y'[x] - x*Sin[y[x]/x] - y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 x \operatorname {ArcTan}\left (e^{c_1} x\right ) \\ y(x)\to 0 \\ y(x)\to \pi x (-1)^{\left \lfloor \frac {1}{2}-\frac {\arg (x)}{\pi }\right \rfloor } \\ \end{align*}