55.25.32 problem 32

Internal problem ID [13741]
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 : 32
Date solved : Thursday, October 02, 2025 at 06:56:04 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (\left (a_{2} x^{2}+a_{1} x +a_{0} \right ) y+b_{2} x^{2}+b_{1} x +b_{0} \right ) y^{\prime }&=c_{2} y^{2}+c_{1} y+c_{0} \end{align*}

✗ Maple

ode:=((a__2*x^2+a__1*x+a__0)*y(x)+b__2*x^2+b__1*x+b__0)*diff(y(x),x) = c__2*y(x)^2+c__1*y(x)+c__0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=((a2*x^2+a1*x+a0)*y[x]+b2*x^2+b1*x+b0)*D[y[x],x]==c2*y[x]^2+c1*y[x]+c0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
a2 = symbols("a2") 
a1 = symbols("a1") 
a0 = symbols("a0") 
b2 = symbols("b2") 
b1 = symbols("b1") 
b0 = symbols("b0") 
c2 = symbols("c2") 
c1 = symbols("c1") 
c0 = symbols("c0") 
y = Function("y") 
ode = Eq(-c0 - c1*y(x) - c2*y(x)**2 + (b0 + b1*x + b2*x**2 + (a0 + a1*x + a2*x**2)*y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out