Internal problem ID [4414]
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: 0.015 (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: 89
DSolve[y'[x]-1/x*Sqrt[1+(y'[x])^2]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )-\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )+2 c_1\right ) \\ y(x)\to \frac {1}{2} \left (-\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )+\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )+2 c_1\right ) \\ \end{align*}