55.24.27 problem 27

Internal problem ID [13656]
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 : 27
Date solved : Wednesday, October 01, 2025 at 11:36:02 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }+\frac {3 a \left (7+3 x \right ) y}{10 x^{{13}/{10}}}&=-\frac {a^{2} \left (x -1\right ) \left (x +9\right )}{5 x^{{8}/{5}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+3/10*a*(3*x+7)/x^(13/10)*y(x) = -1/5*a^2*(x-1)*(9+x)/x^(8/5); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+3/10*a*(3*x+7)*x^(-13/10)*y[x]==-1/5*a^2*(x-1)*(x+9)*x^(-8/5); 
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(a**2*(x - 1)*(x + 9)/(5*x**(8/5)) + 3*a*(3*x + 7)*y(x)/(10*x**(13/10)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out