55.25.33 problem 33

Internal problem ID [13742]
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 : 33
Date solved : Thursday, October 02, 2025 at 07:38:11 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (\left (12 a^{2} x^{2}-7 a x +1\right ) y+4 c \,x^{2}-5 b x \right ) y^{\prime }&=-2 x \left (3 a^{2} y^{2}+2 c y+3 b^{2}\right ) \end{align*}

✗ Maple

ode:=((12*a^2*x^2-7*a*x+1)*y(x)+4*c*x^2-5*b*x)*diff(y(x),x) = -2*x*(3*a^2*y(x)^2+2*c*y(x)+3*b^2); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=((12*a^2*x^2-7*a*x+1)*y[x]+4*c*x^2-5*b*x)*D[y[x],x]==-2*x*(3*a^2*y[x]^2+2*c*y[x]+3*b^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
c = symbols("c") 
b = symbols("b") 
y = Function("y") 
ode = Eq(2*x*(3*a**2*y(x)**2 + 3*b**2 + 2*c*y(x)) + (-5*b*x + 4*c*x**2 + (12*a**2*x**2 - 7*a*x + 1)*y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out