Internal problem ID [1906]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 6, page 25
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y^{\prime } x -y+\sqrt {-x^{2}+y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x*diff(y(x),x)-y(x)+sqrt(y(x)^2-x^2)=0,y(x), singsol=all)
\[ y \left (x \right )+\sqrt {y \left (x \right )^{2}-x^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.362 (sec). Leaf size: 16
DSolve[x*y'[x]-y[x]+Sqrt[y[x]^2-x^2]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x \cosh (-\log (x)+c_1) \]