23.4.28 problem 28

Internal problem ID [6330]
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 : 28
Date solved : Tuesday, September 30, 2025 at 02:47:32 PM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}] == f3[x] + f2[x]*y[x]^2 + (f1[x] - 2*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(-(f1(x) - 2*y(x))*Derivative(y(x), x) - f2(x)*y(x)**2 - f3(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-f2(x)*y(x)**2 - f3(x) + Derivative(y(x),