60.7.69 problem 1660 (book 6.69)

Internal problem ID [11658]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1660 (book 6.69)
Date solved : Monday, January 27, 2025 at 11:29:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

dsolve(diff(diff(y(x),x),x)-y(x)*f(x,diff(y(x),x)/y(x))=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved