Internal problem ID [7702]
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]
\[ \boxed {y^{\prime } x -x \sin \left (\frac {y}{x}\right )-y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
dsolve(x*diff(y(x),x) - x*sin(y(x)/x) - y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \arctan \left (\frac {2 x c_{1}}{c_{1}^{2} x^{2}+1}, -\frac {c_{1}^{2} x^{2}-1}{c_{1}^{2} x^{2}+1}\right ) x \]
✓ Solution by Mathematica
Time used: 2.835 (sec). Leaf size: 33
DSolve[x*y'[x] - x*Sin[y[x]/x] - y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 x \arctan \left (e^{c_1} x\right ) \\ y(x)\to 0 \\ y(x)\to \pi \sqrt {x^2} \\ \end{align*}