55.24.55 problem 55

Internal problem ID [13684]
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 : 55
Date solved : Thursday, October 02, 2025 at 12:43:26 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-\frac {3 a y}{x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{{5}/{2}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)-3*a/x^(7/4)*y(x) = 1/4*a^2*(x-1)*(x-9)/x^(5/2); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-3*a*x^(-7/4)*y[x]==1/4*a^2*(x-1)*(x-9)*x^(-5/2); 
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 - 9)*(x - 1)/(4*x**(5/2)) - 3*a*y(x)/x**(7/4) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out