61.22.56 problem 56

Internal problem ID [12302]
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 : 56
Date solved : Wednesday, March 05, 2025 at 06:35:33 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=\frac {15 x}{4}+\frac {A}{x^{7}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)-y(x) = 15/4*x+A/x^7; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==15/4*x+A*x^(-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(-A/x**7 - 15*x/4 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -A/(x**7*y(x)) - 15*x/(4*y(x)) + Derivative(y(x), x) - 1 cannot be solved by the factorable group method