31.6.9 problem 9

Internal problem ID [5758]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 7
Problem number : 9
Date solved : Monday, January 27, 2025 at 01:12:54 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-\frac {\sqrt {1+{y^{\prime }}^{2}}}{x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.069 (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[D[y[x],x]-1/x*Sqrt[1+(D[y[x],x])^2]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\log \left (\sqrt {x^2-1}+x\right )+c_1 \\ y(x)\to \log \left (\sqrt {x^2-1}+x\right )+c_1 \\ \end{align*}