Internal problem ID [3905]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 9.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\frac {\sqrt {1+{y^{\prime }}^{2}}}{x}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 33
dsolve(diff(y(x),x)-1/x*sqrt(1+(diff(y(x),x))^2)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \ln \left (x +\sqrt {x^{2}-1}\right )+c_{1} \\ y \left (x \right ) = -\ln \left (x +\sqrt {x^{2}-1}\right )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 41
DSolve[y'[x]-1/x*Sqrt[1+(y'[x])^2]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {arctanh}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1 \\ y(x)\to \text {arctanh}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1 \\ \end{align*}