Internal problem ID [4430]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson
7
Problem number: First order with homogeneous Coefficients. Exercise 7.5, page
61.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
dsolve(x*diff(y(x),x)-y(x)-x*sin(y(x)/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: 0.325 (sec). Leaf size: 52
DSolve[x*y'[x]-y[x]-x*Sin[y[x]/x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \arccos (-\tanh (\log (x)+c_1)) y(x)\to x \arccos (-\tanh (\log (x)+c_1)) y(x)\to 0 y(x)\to -\pi x y(x)\to \pi x \end{align*}