54.7.33 problem 1623 (6.33)

Internal problem ID [12882]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1623 (6.33)
Date solved : Wednesday, October 01, 2025 at 02:44:26 AM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+y^{2} f \left (x \right )+y \left (f^{\prime }\left (x \right )+2 f \left (x \right )^{2}\right )&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+(y(x)+3*f(x))*diff(y(x),x)-y(x)^3+y(x)^2*f(x)+y(x)*(diff(f(x),x)+2*f(x)^2) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=f[x]*y[x]^2 - y[x]^3 + y[x]*(2*f[x]^2 + Derivative[1][f][x]) + (3*f[x] + y[x])*D[y[x],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") 
y = Function("y") 
f = Function("f") 
ode = Eq((3*f(x) + y(x))*Derivative(y(x), x) + (2*f(x)**2 + Derivative(f(x), x))*y(x) + f(x)*y(x)**2 - y(x)**3 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-2*f(x)**2*y(x) - f(x)*y(x)**2 + y(x)**3 - y(x)*Derivative(f(x), x) - Derivative(y(x), (x, 2)))/(3*f(x) + y(x)) cannot be solved by the factorable group method