61.22.10 problem 10

Internal problem ID [12256]
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 : 10
Date solved : Monday, March 31, 2025 at 04:55:41 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out