61.22.70 problem 70

Internal problem ID [12316]
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 : 70
Date solved : Monday, March 31, 2025 at 05:08:42 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=-\frac {21 x}{100}+\frac {7 A^{2} \left (\frac {123}{x^{{1}/{7}}}+\frac {280 A}{x^{{5}/{7}}}-\frac {400 A^{2}}{x^{{9}/{7}}}\right )}{9} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)-y(x) = -21/100*x+7/9*A^2*(123/x^(1/7)+280*A/x^(5/7)-400*A^2/x^(9/7)); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==-21/100*x+7/9*A^2*(123*x^(-1/7)+280*A*x^(-5/7)-400*A^2*x^(-9/7)); 
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(-7*A**2*(-400*A**2/x**(9/7) + 280*A/x**(5/7) + 123/x**(1/7))/9 + 21*x/100 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out