23.4.9 problem 9

Internal problem ID [6311]
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 : 9
Date solved : Tuesday, September 30, 2025 at 02:45:44 PM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}] == f[x] + g[x]*y[x] + 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(-f(x) - g(x)*y(x) - 2*y(x)**3 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve -f(x) - g(x)*y(x) - 2*y(x)**3 + Derivative(y(x), (x, 2))