55.22.72 problem 72

Internal problem ID [13613]
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 : 72
Date solved : Wednesday, October 01, 2025 at 07:13:13 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==-(m+1)/(m+2)^2*x+A*x^(2*m+1)+B*x^(3*m+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") 
m = symbols("m") 
y = Function("y") 
ode = Eq(-A*x**(2*m + 1) - B*x**(3*m + 1) + x*(m + 1)/(m + 2)**2 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out