55.25.17 problem 17

Internal problem ID [13726]
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 : 17
Date solved : Thursday, October 02, 2025 at 04:34:26 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out