23.4.23 problem 23

Internal problem ID [6325]
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 : 23
Date solved : Friday, October 03, 2025 at 02:01:17 AM
CAS classification : [NONE]

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

✓ Maple. Time used: 0.049 (sec). Leaf size: 460

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Mathematica

ode=D[y[x],{x,2}] == f[x]*y[x]^2 + y[x]^3 + y[x]*(-2*f[x]^2 + D[f[x],x]) + (3*f[x] - y[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) - 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 -