55.25.8 problem 8

Internal problem ID [13717]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.3. Abel Equations of the Second Kind. subsection 1.3.4-2.
Problem number : 8
Date solved : Sunday, October 12, 2025 at 04:44:53 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 2 x y y^{\prime }&=\left (1-n \right ) y^{2}+\left (a \left (2 n +1\right ) x +2 n -1\right ) y-a^{2} n \,x^{2}-b x -n \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 4278

ode:=2*x*y(x)*diff(y(x),x) = (-n+1)*y(x)^2+(a*(2*n+1)*x+2*n-1)*y(x)-a^2*n*x^2-b*x-n; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✗ Mathematica

ode=2*x*y[x]*D[y[x],x]==(1-n)*y[x]^2+(a*(2*n+1)*x+2*n-1)*y[x]-a^2*n*x^2-b*x-n; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
n = symbols("n") 
y = Function("y") 
ode = Eq(a**2*n*x**2 + b*x + n + 2*x*y(x)*Derivative(y(x), x) - (1 - n)*y(x)**2 - (a*x*(2*n + 1) + 2*n - 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out