23.4.24 problem 24

Internal problem ID [6326]
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 : 24
Date solved : Tuesday, September 30, 2025 at 02:47:25 PM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }&=\operatorname {f2} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f1} \left (x \right ) y^{2}+y^{3}+\left (3 \operatorname {f1} \left (x \right )-y\right ) y^{\prime } \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x) = f2(x)+f3(x)*y(x)+f1(x)*y(x)^2+y(x)^3+(3*f1(x)-y(x))*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}] == f2[x] + f3[x]*y[x] + f1[x]*y[x]^2 + y[x]^3 + (3*f1[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*f1(x) - y(x))*Derivative(y(x), x) - f1(x)*y(x)**2 - f2(x) - f3(x)*y(x) - 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) - (-f1(x)*y(x)**2 - f2(x) - f3(x)*y(x) - y(x