Internal problem ID [9239]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1661 (book 6.70).
ODE order: 2.
ODE degree: -1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-x^{n -2} f \left (y x^{-n}, y^{\prime } x^{-n +1}\right )=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x)-x^(n-2)*f(y(x)/(x^n),diff(y(x),x)/(x^(n-1)))=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-(x^(-2 + n)*f[y[x]/x^n, x^(1 - n)*y'[x]]) + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved