55.25.22 problem 22

Internal problem ID [13731]
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 : 22
Date solved : Sunday, October 12, 2025 at 04:49:15 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (A x y+B \,x^{2}+a_{1} x +b_{1} y+c_{1} \right ) y^{\prime }&=A y^{2}+B x y+a_{2} x +b_{2} y+c_{2} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 167096

ode:=(A*x*y(x)+B*x^2+a__1*x+b__1*y(x)+c__1)*diff(y(x),x) = A*y(x)^2+B*x*y(x)+a__2*x+b__2*y(x)+c__2; 
dsolve(ode,y(x), singsol=all);
 

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

✗ Mathematica

ode=(A*x*y[x]+B*x^2+a1*x+b1*y[x]+c1)*D[y[x],x]==A*y[x]^2+B*x*y[x]+a2*x+b2*y[x]+c2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
A = symbols("A") 
B = symbols("B") 
a1 = symbols("a1") 
a2 = symbols("a2") 
b1 = symbols("b1") 
b2 = symbols("b2") 
c1 = symbols("c1") 
c2 = symbols("c2") 
y = Function("y") 
ode = Eq(-A*y(x)**2 - B*x*y(x) - a2*x - b2*y(x) - c2 + (A*x*y(x) + B*x**2 + a1*x + b1*y(x) + c1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out