55.24.22 problem 22

Internal problem ID [13651]
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 : 22
Date solved : Wednesday, October 01, 2025 at 11:05:46 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }+\frac {5 a \left (23 x -16\right ) y}{56 x^{{9}/{7}}}&=-\frac {3 a^{2} \left (x -1\right ) \left (25 x -32\right )}{56 x^{{11}/{17}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+5/56*a*(23*x-16)/x^(9/7)*y(x) = -3/56*a^2*(x-1)*(25*x-32)/x^(11/17); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+5/56*a*(23*x-16)*x^(-9/7)*y[x]==-3/56*a^2*(x-1)*(25*x-32)*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 - 1)*(25*x - 32)/(56*x**(11/17)) + 5*a*(23*x - 16)*y(x)/(56*x**(9/7)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out