55.24.57 problem 57

Internal problem ID [13686]
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 : 57
Date solved : Thursday, October 02, 2025 at 12:45:53 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out