Internal problem ID [5768]
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: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y^{\prime } x -y-\sqrt {y^{2}-x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(x*diff(y(x),x)=y(x)+sqrt(y(x)^2-x^2),y(x), singsol=all)
\[ \frac {y \left (x \right )}{x^{2}}+\frac {\sqrt {y \left (x \right )^{2}-x^{2}}}{x^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.366 (sec). Leaf size: 14
DSolve[x*y'[x]==y[x]+Sqrt[y[x]^2-x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x \cosh (\log (x)+c_1) \]