55.24.12 problem 12

Internal problem ID [13641]
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 : 12
Date solved : Wednesday, October 01, 2025 at 09:42:47 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out