55.22.65 problem 65

Internal problem ID [13606]
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 1.3.1-2. Solvable equations and their solutions
Problem number : 65
Date solved : Sunday, October 12, 2025 at 04:09:12 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=-\frac {6 x}{25}+\frac {4 B^{2} \left (\left (2-A \right ) x^{{1}/{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{{1}/{3}}}-\frac {A \,B^{3}}{x^{{2}/{3}}}\right )}{75} \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 3187

ode:=y(x)*diff(y(x),x)-y(x) = -6/25*x+4/75*B^2*((-A+2)*x^(1/3)-3/2*B*(2*A+1)+B^2*(1-3*A)/x^(1/3)-A*B^3/x^(2/3)); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==-6/25*x+4/75*B^2*((2-A)*x^(1/3)-3/2*B*(2*A+1)+B^2*(1-3*A)*x^(-1/3)-A*B^3*x^(-2/3)); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
A = symbols("A") 
B = symbols("B") 
y = Function("y") 
ode = Eq(-4*B**2*(-A*B**3/x**(2/3) + B**2*(1 - 3*A)/x**(1/3) - 3*B*(2*A + 1)/2 + x**(1/3)*(2 - A))/75 + 6*x/25 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out