55.22.39 problem 39

Internal problem ID [13580]
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 : 39
Date solved : Wednesday, October 01, 2025 at 06:02:43 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=-\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)-y(x) = -6/25*x+6/25*A*(2*x^(1/2)+7*A+4*A^2/x^(1/2)); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==-6/25*x+6/25*A*(2*x^(1/2)+7*A+4*A^2*x^(-1/2)); 
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(-6*A*(4*A**2/sqrt(x) + 7*A + 2*sqrt(x))/25 + 6*x/25 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (24*A**3 + 6*sqrt(x)*(7*A**2 + 2*A*sqrt(x) - x) + 25*sqrt(x)*y(x))/(25*sqrt(x)*y(x)) cannot be solved by the factorable group method