61.24.10 problem 10

Internal problem ID [12344]
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 : 10
Date solved : Monday, March 31, 2025 at 05:11:33 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out