Internal problem ID [4040]
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]
\[ \boxed {y^{\prime } x -x \sin \left (\frac {y}{x}\right )-y=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 2.767 (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*}