61.22.6 problem 6

Internal problem ID [12252]
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 1.3.1-2. Solvable equations and their solutions
Problem number : 6
Date solved : Monday, March 31, 2025 at 04:55:29 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y y^{\prime }-y&=A \,x^{k -1}-k B \,x^{k}+k \,B^{2} x^{2 k -1} \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==A*x^(k-1)-k*B*x^k+k*B^2*x^(2*k-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") 
k = symbols("k") 
y = Function("y") 
ode = Eq(-A*x**(k - 1) - B**2*k*x**(2*k - 1) + B*k*x**k + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ZeroDivisionError : polynomial division