54.7.117 problem 1730 (book 6.139)

Internal problem ID [12966]
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 : Wednesday, October 01, 2025 at 02:55:25 AM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
f = Function("f") 
ode = Eq(a + f(x)*y(x)**2 + 2*y(x)*Derivative(y(x), (x, 2)) - Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt(a + f(x)*y(x)**2 + 2*y(x)*Derivative(y(x), (x, 2))) + Derivative(y(x), x) cannot be solved by the factorable group method