55.24.50 problem 50

Internal problem ID [13679]
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 : 50
Date solved : Thursday, October 02, 2025 at 12:33:47 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Timed Out