Internal problem ID [5001]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {x y^{\prime }-y-\tan \left (\frac {y}{x}\right ) x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 10
dsolve(x*diff(y(x),x)-y(x)=x*tan(y(x)/x),y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (c_{1} x \right ) x \]
✓ Solution by Mathematica
Time used: 0.934 (sec). Leaf size: 19
DSolve[x*y'[x]-y[x]==x*Tan[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \text {ArcSin}\left (e^{c_1} x\right ) \\ y(x)\to 0 \\ \end{align*}