61.22.67 problem 67

Internal problem ID [12313]
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 1.3.1-2. Solvable equations and their solutions
Problem number : 67
Date solved : Wednesday, March 05, 2025 at 06:37:11 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=-\frac {6 x}{25}+\frac {7 A \,x^{{1}/{3}}}{5}+\frac {31 A^{2}}{3 x^{{1}/{3}}}-\frac {100 A^{4}}{3 x^{{5}/{3}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)-y(x) = -6/25*x+7/5*A*x^(1/3)+31/3*A^2/x^(1/3)-100/3*A^4/x^(5/3); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==-6/25*x+7/5*A*x^(1/3)+31/3*A^2*x^(-1/3)-100/3*A^4*x^(-5/3); 
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(100*A**4/(3*x**(5/3)) - 31*A**2/(3*x**(1/3)) - 7*A*x**(1/3)/5 + 6*x/25 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out