55.24.28 problem 28

Internal problem ID [13657]
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 : 28
Date solved : Sunday, October 12, 2025 at 04:21:08 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{{9}/{5}}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 669

ode:=y(x)*diff(y(x),x)+1/10*a*(7*x-12)/x^(7/5)*y(x) = -1/10*a^2*(x-1)*(x-16)/x^(9/5); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Mathematica

ode=y[x]*D[y[x],x]+1/10*a*(7*x-12)*x^(-7/5)*y[x]==-1/10*a^2*(x-1)*(x-16)*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(a**2*(x - 16)*(x - 1)/(10*x**(9/5)) + a*(7*x - 12)*y(x)/(10*x**(7/5)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out