55.24.23 problem 23

Internal problem ID [13652]
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 : 23
Date solved : Wednesday, October 01, 2025 at 11:26:05 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }+\frac {a \left (19 x +85\right ) y}{26 x^{{18}/{13}}}&=-\frac {3 a^{2} \left (x -1\right ) \left (x +25\right )}{26 x^{{23}/{13}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+1/26*a*(19*x+85)/x^(18/13)*y(x) = -3/26*a^2*(x-1)*(x+25)/x^(23/13); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+1/26*a*(19*x+85)*x^(-18/13)*y[x]==-3/26*a^2*(x-1)*(x+25)*x^(-23/13); 
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)*(x + 25)/(26*x**(23/13)) + a*(19*x + 85)*y(x)/(26*x**(18/13)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out