61.25.5 problem 5

Internal problem ID [12419]
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 1.3.4-2.
Problem number : 5
Date solved : Monday, March 31, 2025 at 05:33:48 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=(y[x]+a*x^(n+1)+b*x^n)*D[y[x],x]==(a*n*x^n+c*x^(n-1))*y[x]; 
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") 
n = symbols("n") 
y = Function("y") 
ode = Eq((-a*n*x**n - c*x**(n - 1))*y(x) + (a*x**(n + 1) + b*x**n + y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out