55.24.63 problem 63

Internal problem ID [13692]
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 : 63
Date solved : Thursday, October 02, 2025 at 01:56:45 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out