Internal problem ID [9397]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1819 (book 6.228).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (y^{\prime } x -y\right ) y^{\prime \prime }-\left (\left (y^{\prime }\right )^{2}+1\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 66
dsolve((x*diff(y(x),x)-y(x))*diff(diff(y(x),x),x)-(diff(y(x),x)^2+1)^2=0,y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-\ln \relax (x )+\int _{}^{\textit {\_Z}}\frac {-\textit {\_f} +\RootOf \left (-\tan \left (\frac {1}{\textit {\_Z}}\right ) c_{1} \textit {\_Z} +\textit {\_f} c_{1} \tan \left (\frac {1}{\textit {\_Z}}\right )+\tan \left (\frac {1}{\textit {\_Z}}\right ) \textit {\_Z} \textit {\_f} +c_{1} \textit {\_Z} \textit {\_f} +\tan \left (\frac {1}{\textit {\_Z}}\right )+c_{1}+\textit {\_Z} -\textit {\_f} \right )}{\textit {\_f}^{2}+1}d \textit {\_f} +c_{2}\right ) x \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-(1 + y'[x]^2)^2 + (-y[x] + x*y'[x])*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved