29.37.7 problem 1120

Internal problem ID [5665]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1120
Date solved : Monday, January 27, 2025 at 01:02:23 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.087 (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: 0.008 (sec). Leaf size: 41

DSolve[Sqrt[1+(D[y[x],x])^2]==x*D[y[x],x],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*}