Internal problem ID [15116]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8.3. The Lagrange and Clairaut equations. Exercises page 72
Problem number: 228.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y-x y^{\prime }-a \sqrt {1+{y^{\prime }}^{2}}=0} \]
✓ Solution by Maple
Time used: 0.391 (sec). Leaf size: 17
dsolve(y(x)=x*diff(y(x),x)+a*sqrt(1+diff(y(x),x)^2),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x +a \sqrt {c_{1}^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 27
DSolve[y[x]==x*y'[x]+a*Sqrt[1+y'[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to a \sqrt {1+c_1{}^2}+c_1 x \\ y(x)\to a \\ \end{align*}