55.22.68 problem 68

Internal problem ID [13609]
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 : 68
Date solved : Wednesday, October 01, 2025 at 07:03:29 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=-\frac {10 x}{49}+\frac {13 A^{2}}{5 x^{{1}/{5}}}-\frac {7 A^{3}}{20 x^{{4}/{5}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)-y(x) = -10/49*x+13/5*A^2/x^(1/5)-7/20*A^3/x^(4/5); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==-10/49*x+13/5*A^2*x^(-1/5)-7/20*A^3*x^(-4/5); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
A = symbols("A") 
y = Function("y") 
ode = Eq(7*A**3/(20*x**(4/5)) - 13*A**2/(5*x**(1/5)) + 10*x/49 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out