55.25.21 problem 21

Internal problem ID [13730]
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 : 21
Date solved : Sunday, October 12, 2025 at 04:47:44 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (A x y+A k y+B \,x^{2}+B k x \right ) y^{\prime }&=c y^{2}+d x y+k \left (d -B \right ) y \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 770

ode:=(A*x*y(x)+A*k*y(x)+B*x^2+B*k*x)*diff(y(x),x) = c*y(x)^2+d*x*y(x)+k*(d-B)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Mathematica

ode=(A*x*y[x]+A*k*y[x]+B*x^2+B*k*x)*D[y[x],x]==c*y[x]^2+d*x*y[x]+k*(d-B)*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
A = symbols("A") 
k = symbols("k") 
B = symbols("B") 
c = symbols("c") 
d = symbols("d") 
y = Function("y") 
ode = Eq(-c*y(x)**2 - d*x*y(x) - k*(-B + d)*y(x) + (A*k*y(x) + A*x*y(x) + B*k*x + B*x**2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out