23.4.21 problem 21

Internal problem ID [6323]
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 : 21
Date solved : Tuesday, September 30, 2025 at 02:47:09 PM
CAS classification : [NONE]

\begin{align*} y y^{\prime }+y^{\prime \prime }&=-12 f \left (x \right ) y+y^{3}+12 f^{\prime }\left (x \right ) \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+diff(diff(y(x),x),x) = -12*f(x)*y(x)+y(x)^3+12*diff(f(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x] + D[y[x],{x,2}] == -12*f[x]*y[x] + y[x]^3 + 12*D[f[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*f(x)*y(x) - y(x)**3 + y(x)*Derivative(y(x), x) - 12*Derivative(f(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -((-12*f(x) + y(x)**2)*y(x) + 12*Derivative(f(x), x) - Derivativ