Internal problem ID [5006]
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: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x y^{\prime }-\sqrt {x^{2}-y^{2}}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(x*diff(y(x),x)-sqrt(x^2-y(x)^2)-y(x)=0,y(x), singsol=all)
\[ -\arctan \left (\frac {y \relax (x )}{\sqrt {x^{2}-y \relax (x )^{2}}}\right )+\ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.707 (sec). Leaf size: 17
DSolve[x*y'[x]-Sqrt[x^2-y[x]^2]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \cosh (i \log (x)+c_1) \\ \end{align*}