54.7.8 problem 1598 (6.8)

Internal problem ID [12857]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1598 (6.8)
Date solved : Wednesday, October 01, 2025 at 02:22:39 AM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }-2 a^{2} y^{3}+2 a b x y-b&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)-2*a^2*y(x)^3+2*a*b*x*y(x)-b = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=-b + 2*a*b*x*y[x] - 2*a^2*y[x]^3 + D[y[x],{x,2}] == 0; 
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**2*y(x)**3 + 2*a*b*x*y(x) - b + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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