61.24.4 problem 4

Internal problem ID [12338]
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 : 4
Date solved : Monday, March 31, 2025 at 05:11:11 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

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

✗ Maple

ode:=y(x)*diff(y(x),x) = ((3-m)*x-1)*y(x)-(m-1)*a*x; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]==((3-m)*x-1)*y[x]+(m-1)*(x^2-x^2-a*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
m = symbols("m") 
y = Function("y") 
ode = Eq(a*x*(m - 1) - (x*(3 - m) - 1)*y(x) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out