Internal problem ID [4041]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.28, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -x \sin \left (\frac {y}{x}\right )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 44
dsolve(x*diff(y(x),x)-x*sin(y(x)/x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \arctan \left (\frac {2 x c_{1}}{x^{2} c_{1}^{2}+1}, -\frac {x^{2} c_{1}^{2}-1}{x^{2} c_{1}^{2}+1}\right ) x \]
✓ Solution by Mathematica
Time used: 2.633 (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 \text {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*}