Internal problem ID [8892]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 557.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {x \left (\sqrt {{y^{\prime }}^{2}+1}+y^{\prime }\right )-y=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 97
dsolve(x*((diff(y(x),x)^2+1)^(1/2)+diff(y(x),x))-y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x \left (\sqrt {-x \left (-2 c_{1} +x \right )}\, \sqrt {-\frac {c_{1}^{2}}{x \left (-2 c_{1} +x \right )}}-x +c_{1} \right )}{\sqrt {-x \left (-2 c_{1} +x \right )}} \\ y \left (x \right ) &= \frac {x \left (\sqrt {-x \left (-2 c_{1} +x \right )}\, \sqrt {-\frac {c_{1}^{2}}{x \left (-2 c_{1} +x \right )}}+x -c_{1} \right )}{\sqrt {-x \left (-2 c_{1} +x \right )}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.272 (sec). Leaf size: 37
DSolve[-y[x] + x*(y'[x] + Sqrt[1 + y'[x]^2])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x (x-c_1)} \\ y(x)\to \sqrt {-x (x-c_1)} \\ \end{align*}