23.4.121 problem 121

Internal problem ID [6423]
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 : 121
Date solved : Tuesday, September 30, 2025 at 02:56:31 PM
CAS classification : [NONE]

\begin{align*} f \left (x \right )^{2} y^{\prime \prime }&=-24 f \left (x \right )^{4}+\left (3 f \left (x \right )^{3}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right )\right ) y^{\prime } \end{align*}

✗ Maple

ode:=f(x)^2*diff(diff(y(x),x),x) = -24*f(x)^4+(3*f(x)^3-f(x)^2*y(x)+3*f(x)*diff(f(x),x))*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=f[x]^2*D[y[x],{x,2}] == -24*f[x]^4 + (3*f[x]^3 - f[x]^2*y[x] + 3*f[x]*D[f[x],x])*D[y[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(-(3*f(x)**3 - f(x)**2*y(x) + 3*f(x)*Derivative(f(x), x))*Derivative(y(x), x) + 24*f(x)**4 + f(x)**2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -24*f(x)**3 + 3*f(x)**2*Derivative(y(x), x) - f(x)*y(x)*Derivati