23.4.10 problem 10

Internal problem ID [6312]
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 : 10
Date solved : Tuesday, September 30, 2025 at 02:45:45 PM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }&=a -2 a b x y+2 b^{2} y^{3} \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : solve: Cannot solve 2*a*b*x*y(x) - a - 2*b**2*y(x)**3 + Derivative(y(x), (x, 2