55.24.26 problem 26

Internal problem ID [13655]
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 : 26
Date solved : Wednesday, October 01, 2025 at 11:32:30 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y y^{\prime }+\frac {3 a \left (19 x -14\right ) x^{{7}/{5}} y}{35}&=-\frac {4 a^{2} \left (x -1\right ) \left (9 x -14\right ) x^{{9}/{5}}}{35} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+3/35*a*(19*x-14)*x^(7/5)*y(x) = -4/35*a^2*(x-1)*(9*x-14)*x^(9/5); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+3/35*a*(19*x-14)*x^(7/5)*y[x]==-4/35*a^2*(x-1)*(9*x-14)*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(4*a**2*x**(9/5)*(x - 1)*(9*x - 14)/35 + 3*a*x**(7/5)*(19*x - 14)*y(x)/35 + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out