55.24.54 problem 54

Internal problem ID [13683]
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 : 54
Date solved : Thursday, October 02, 2025 at 12:40:48 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }+\frac {a \left (21 x +19\right ) y}{5 x^{{7}/{5}}}&=-\frac {2 a^{2} \left (x -1\right ) \left (9 x -4\right )}{5 x^{{9}/{5}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+1/5*a*(21*x+19)/x^(7/5)*y(x) = -2/5*a^2*(x-1)*(9*x-4)/x^(9/5); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+1/5*a*(21*x+19)*x^(-7/5)*y[x]==-2/5*a^2*(x-1)*(9*x-4)*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(2*a**2*(x - 1)*(9*x - 4)/(5*x**(9/5)) + a*(21*x + 19)*y(x)/(5*x**(7/5)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out