Internal problem ID [12484]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 95.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]
\[ \boxed {y-y^{\prime } x -\sqrt {-{y^{\prime }}^{2}+1}=0} \]
✓ Solution by Maple
Time used: 0.344 (sec). Leaf size: 17
dsolve(y(x)=x*diff(y(x),x)+sqrt(1-diff(y(x),x)^2),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x +\sqrt {-c_{1}^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.08 (sec). Leaf size: 27
DSolve[y[x]==x*y'[x]+Sqrt[1-y'[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x+\sqrt {1-c_1{}^2} \\ y(x)\to 1 \\ \end{align*}