55.24.37 problem 37

Internal problem ID [13666]
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 : 37
Date solved : Thursday, October 02, 2025 at 12:03:56 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (8 x -5\right )}{5 x^{7}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)-2/5*a*(3*x-10)/x^4*y(x) = 1/5*a^2*(x-1)*(8*x-5)/x^7; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-2/5*a*(3*x-10)*x^(-4)*y[x]==1/5*a^2*(x-1)*(8*x-5)*x^(-7); 
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)*(8*x - 5)/(5*x**7) - 2*a*(3*x - 10)*y(x)/(5*x**4) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out