23.4.17 problem 17

Internal problem ID [6319]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 17
Date solved : Tuesday, September 30, 2025 at 02:46:47 PM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*(2*f[x]^2 + D[f[x],x]) + 3*f[x]*D[y[x],x] + D[y[x],{x,2}] == 2*y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*f(x)**2 + Derivative(f(x), x))*y(x) + 3*f(x)*Derivative(y(x), x) - 2*y(x)**3 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(-2*f(x)**2*y(x) + 2*y(x)**3 - y(x)*Derivative(f(x), x) - Deriv