Internal problem ID [15136]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 11. Singular solutions of differential equations. Exercises page 92
Problem number: 274.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]
\[ \boxed {y-x y^{\prime }-\sqrt {a^{2} {y^{\prime }}^{2}+b^{2}}=0} \]
✓ Solution by Maple
Time used: 0.266 (sec). Leaf size: 21
dsolve(y(x)=x*diff(y(x),x)+sqrt(a^2*diff(y(x),x)^2+b^2),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x +\sqrt {a^{2} c_{1}^{2}+b^{2}} \]
✓ Solution by Mathematica
Time used: 0.359 (sec). Leaf size: 37
DSolve[y[x]==x*y'[x]+Sqrt[a^2*y'[x]^2+b^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {b^2+a^2 c_1{}^2}+c_1 x \\ y(x)\to \sqrt {b^2} \\ \end{align*}