61.24.21 problem 21

Internal problem ID [12355]
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 : 21
Date solved : Wednesday, March 05, 2025 at 06:46:58 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }+\frac {a \left (13 x -20\right ) y}{14 x^{{9}/{7}}}&=-\frac {3 a^{2} \left (x -1\right ) \left (x -8\right )}{14 x^{{11}/{17}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+1/14*a*(13*x-20)/x^(9/7)*y(x) = -3/14*a^2*(x-1)*(x-8)/x^(11/17); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+1/14*a*(13*x-20)*x^(-9/7)*y[x]==-3/14*a^2*(x-1)*(x-8)*x^(-11/17); 
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(3*a**2*(x - 8)*(x - 1)/(14*x**(11/17)) + a*(13*x - 20)*y(x)/(14*x**(9/7)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out