55.24.24 problem 24

Internal problem ID [13653]
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 : 24
Date solved : Wednesday, October 01, 2025 at 11:29:01 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}}&=-\frac {4 a^{2} \left (x -1\right ) \left (-6+x \right )}{15 x^{{9}/{5}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+1/15*a*(13*x-18)/x^(7/5)*y(x) = -4/15*a^2*(x-1)*(x-6)/x^(9/5); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+1/15*a*(13*x-18)*x^(-7/5)*y[x]==-4/15*a^2*(x-1)*(x-6)*x^(-9/5); 
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(4*a**2*(x - 6)*(x - 1)/(15*x**(9/5)) + a*(13*x - 18)*y(x)/(15*x**(7/5)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out