Internal problem ID [3911]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 14.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y-x y^{\prime }-x \sqrt {1+\left (y^{\prime }\right )^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.202 (sec). Leaf size: 78
dsolve(y(x)=x*diff(y(x),x)+x*sqrt(1+(diff(y(x),x))^2),y(x), singsol=all)
\[ \frac {c_{1}}{\left (-\frac {x^{2}-y \relax (x )^{2}}{2 x y \relax (x )}+\frac {\sqrt {\frac {x^{4}+2 x^{2} y \relax (x )^{2}+y \relax (x )^{4}}{x^{2} y \relax (x )^{2}}}}{2}\right ) \sqrt {\frac {\left (x^{2}+y \relax (x )^{2}\right )^{2}}{x^{2} y \relax (x )^{2}}}}+x = 0 \]
✓ Solution by Mathematica
Time used: 0.192 (sec). Leaf size: 35
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*}