55.25.13 problem 13

Internal problem ID [13722]
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 : 13
Date solved : Thursday, October 02, 2025 at 04:27:42 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
A = symbols("A") 
m = symbols("m") 
y = Function("y") 
ode = Eq(-x - (1/2 - m/2)*y(x)**2 - (m - 1)*y(x)/(m + 3) + (A*(1 - m)*y(x) + 2*x*y(x) - x*(2*m + 2)/(m + 3))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out