60.7.70 problem 1661 (book 6.70)

Internal problem ID [11659]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1661 (book 6.70)
Date solved : Monday, January 27, 2025 at 11:29:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-x^{n -2} f \left (y x^{-n}, y^{\prime } x^{-n +1}\right )&=0 \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[-(x^(-2 + n)*f[y[x]/x^n, x^(1 - n)*D[y[x],x]]) + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved