Internal problem ID [4419]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y-x y^{\prime }-x \sqrt {1+{y^{\prime }}^{2}}=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 97
dsolve(y(x)=x*diff(y(x),x)+x*sqrt(1+(diff(y(x),x))^2),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (\sqrt {-\frac {c_{1}^{2}}{x \left (-2 c_{1} +x \right )}}\, \sqrt {-x \left (-2 c_{1} +x \right )}-x +c_{1} \right ) x}{\sqrt {-x \left (-2 c_{1} +x \right )}} \\ y \left (x \right ) &= \frac {\left (\sqrt {-\frac {c_{1}^{2}}{x \left (-2 c_{1} +x \right )}}\, \sqrt {-x \left (-2 c_{1} +x \right )}+x -c_{1} \right ) x}{\sqrt {-x \left (-2 c_{1} +x \right )}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.269 (sec). Leaf size: 37
DSolve[y[x]==x*y'[x]+x*Sqrt[1+(y'[x])^2],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*}