61.24.34 problem 34

Internal problem ID [12368]
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 : 34
Date solved : Monday, March 31, 2025 at 05:22:14 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }+\frac {a \left (13 x -3\right ) y}{6 x^{{2}/{3}}}&=-\frac {a^{2} \left (x -1\right ) \left (5 x -1\right )}{6 x^{{1}/{3}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+1/6*a*(13*x-3)/x^(2/3)*y(x) = -1/6*a^2*(x-1)*(5*x-1)/x^(1/3); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+1/6*a*(13*x-3)*x^(-2/3)*y[x]==-1/6*a^2*(x-1)*(5*x-1)*x^(-1/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a**2*(x - 1)*(5*x - 1)/(6*x**(1/3)) + a*(13*x - 3)*y(x)/(6*x**(2/3)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out