Internal problem ID [3812]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1120.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {\sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 33
dsolve(sqrt(1+diff(y(x),x)^2) = x*diff(y(x),x),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: 0.009 (sec). Leaf size: 41
DSolve[Sqrt[1+(y'[x])^2]==x y'[x],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*}