61.22.62 problem 62

Internal problem ID [12308]
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 : 62
Date solved : Monday, March 31, 2025 at 05:06:23 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=-\frac {5 x}{36}+\frac {A}{x^{{3}/{5}}}-\frac {B}{x^{{7}/{5}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)-y(x) = -5/36*x+A/x^(3/5)-B/x^(7/5); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==-5/36*x+A*x^(-3/5)-B*x^(-7/5); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
A = symbols("A") 
B = symbols("B") 
y = Function("y") 
ode = Eq(-A/x**(3/5) + B/x**(7/5) + 5*x/36 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out