55.22.66 problem 66

Internal problem ID [13607]
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 : 66
Date solved : Wednesday, October 01, 2025 at 06:58:00 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=\frac {3 x}{4}-\frac {3 A \,x^{{1}/{3}}}{2}+\frac {3 A^{2}}{4 x^{{1}/{3}}}-\frac {27 A^{4}}{625 x^{{5}/{3}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)-y(x) = 3/4*x-3/2*A*x^(1/3)+3/4*A^2/x^(1/3)-27/625*A^4/x^(5/3); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==3/4*x-3/2*A*x^(1/3)+3/4*A^2*x^(-1/3)-27/625*A^4*x^(-5/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
A = symbols("A") 
y = Function("y") 
ode = Eq(27*A**4/(625*x**(5/3)) - 3*A**2/(4*x**(1/3)) + 3*A*x**(1/3)/2 - 3*x/4 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out