61.24.35 problem 35

Internal problem ID [12369]
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 1.3.3-2.
Problem number : 35
Date solved : Wednesday, March 05, 2025 at 06:53:50 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-\frac {a \left (8 x -1\right ) y}{28 x^{{8}/{7}}}&=\frac {a^{2} \left (x -1\right ) \left (32 x +3\right )}{28 x^{{9}/{7}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)-1/28*a*(8*x-1)/x^(8/7)*y(x) = 1/28*a^2*(x-1)*(32*x+3)/x^(9/7); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-1/28*a*(8*x-1)*x^(-8/7)*y[x]==1/28*a^2*(x-1)*(32*x+3)*x^(-9/7); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a**2*(x - 1)*(32*x + 3)/(28*x**(9/7)) - a*(8*x - 1)*y(x)/(28*x**(8/7)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out