Internal problem ID [8890]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 555.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]
\[ \boxed {\sqrt {{y^{\prime }}^{2}+1}+x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.266 (sec). Leaf size: 15
dsolve((diff(y(x),x)^2+1)^(1/2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {c_{1}^{2}+1}+c_{1} x \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 25
DSolve[-y[x] + x*y'[x] + Sqrt[1 + y'[x]^2]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x+\sqrt {1+c_1{}^2} \\ y(x)\to 1 \\ \end{align*}