55.26.8 problem 8

Internal problem ID [13755]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.4. Equations Containing Polynomial Functions of y. subsection 1.4.1-2 Abel equations of the first kind.
Problem number : 8
Date solved : Thursday, October 02, 2025 at 07:58:05 AM
CAS classification : [_Abel]

\begin{align*} y^{\prime }&=a x y^{3}+2 a b \,x^{2} y^{2}-b -2 a \,b^{3} x^{4} \end{align*}

✗ Maple

ode:=diff(y(x),x) = a*x*y(x)^3+2*a*b*x^2*y(x)^2-b-2*a*b^3*x^4; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]==a*x*y[x]^3+2*a*b*x^2*y[x]^2-b-2*a*b^3*x^4; 
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**3*x**4 - 2*a*b*x**2*y(x)**2 - a*x*y(x)**3 + b + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded