Internal problem ID [15011]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 5. Homogeneous equations. Exercises page 44
Problem number: 104.
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: 0.0 (sec). Leaf size: 28
dsolve(x*diff(y(x),x)=y(x)+sqrt(y(x)^2-x^2),y(x), singsol=all)
\[ \frac {-c_{1} x^{2}+y+\sqrt {y^{2}-x^{2}}}{x^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.409 (sec). Leaf size: 14
DSolve[x*y'[x]==y[x]+Sqrt[y[x]^2-x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x \cosh (\log (x)+c_1) \]