55.25.35 problem 35

Internal problem ID [13744]
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 : 35
Date solved : Thursday, October 02, 2025 at 07:48:17 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x \left (2 a x y+b \right ) y^{\prime }&=-4 a \,x^{2} y^{2}-3 b x y+c \,x^{2}+k \end{align*}

✗ Maple

ode:=x*(2*a*x*y(x)+b)*diff(y(x),x) = -4*a*x^2*y(x)^2-3*b*x*y(x)+c*x^2+k; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x*( 2*a*x*y[x]+b)*D[y[x],x]==-4*a*x^2*y[x]^2-3*b*x*y[x]+c*x^2+k; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
k = symbols("k") 
y = Function("y") 
ode = Eq(4*a*x**2*y(x)**2 + 3*b*x*y(x) - c*x**2 - k + x*(2*a*x*y(x) + b)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out