61.24.30 problem 30

Internal problem ID [12364]
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 : 30
Date solved : Wednesday, March 05, 2025 at 06:52:22 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }+\frac {3 a \left (3 x +11\right ) y}{14 x^{{10}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -27\right )}{14 x^{{13}/{7}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+3/14*a*(3*x+11)/x^(10/7)*y(x) = -1/14*a^2*(x-1)*(x-27)/x^(13/7); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+3/14*a*(3*x+11)*x^(-10/7)*y[x]==-1/14*a^2*(x-1)*(x-27)*x^(-13/7); 
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 - 27)*(x - 1)/(14*x**(13/7)) + 3*a*(3*x + 11)*y(x)/(14*x**(10/7)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out