60.7.139 problem 1730 (book 6.139)

Internal problem ID [11728]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1730 (book 6.139)
Date solved : Monday, January 27, 2025 at 11:31:56 PM
CAS classification : [NONE]

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

✗ Solution by Maple

dsolve(2*diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+y(x)^2*f(x)+a=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[a + f[x]*y[x]^2 - D[y[x],x]^2 + 2*y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved