55.25.30 problem 30

Internal problem ID [13739]
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 : 30
Date solved : Thursday, October 02, 2025 at 06:46:58 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (\left (x +c \right ) y+\left (n +1\right ) x^{2}-a \left (1+2 n \right ) x +a^{2} n \right ) y^{\prime }&=\frac {2 n y^{2}}{3 n -1}+2 y x \end{align*}

✗ Maple

ode:=((x+c)*y(x)+(n+1)*x^2-a*(2*n+1)*x+a^2*n)*diff(y(x),x) = 2*n/(3*n-1)*y(x)^2+2*x*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=((x+c)*y[x]+(n+1)*x^2-a*(2*n+1)*x+a^2*n)*D[y[x],x]==2*n/(3*n-1)*y[x]^2+2*x*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
c = symbols("c") 
n = symbols("n") 
y = Function("y") 
ode = Eq(-2*n*y(x)**2/(3*n - 1) - 2*x*y(x) + (a**2*n - a*x*(2*n + 1) + x**2*(n + 1) + (c + x)*y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out