Internal problem ID [1906]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -y+\sqrt {y^{2}-x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 21
dsolve(x*diff(y(x),x)-y(x)+sqrt(y(x)^2-x^2)=0,y(x), singsol=all)
\[ y \relax (x )+\sqrt {y \relax (x )^{2}-x^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.449 (sec). Leaf size: 15
DSolve[x*y'[x]-y[x]+Sqrt[y[x]^2-x^2]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \cosh (-\log (x)+c_1) \\ \end{align*}