55.24.40 problem 40

Internal problem ID [13669]
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 1.3.3-2.
Problem number : 40
Date solved : Thursday, October 02, 2025 at 12:07:38 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }+\frac {a \left (3 x -2\right ) y}{x}&=-\frac {2 a^{2} \left (x -1\right )^{2}}{x} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+a*(3*x-2)/x*y(x) = -2*a^2*(x-1)^2/x; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+a*(3*x-2)*x^(-1)*y[x]==-2*a^2*(x-1)^2*x^(-1); 
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(2*a**2*(x - 1)**2/x + a*(3*x - 2)*y(x)/x + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out