61.22.71 problem 71

Internal problem ID [12317]
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 : 71
Date solved : Monday, March 31, 2025 at 05:09:25 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y y^{\prime }-y&=a x +b \,x^{m} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)-y(x) = a*x+b*x^m; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==a*x+b*x^m; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
m = symbols("m") 
y = Function("y") 
ode = Eq(-a*x - b*x**m + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(a*x + b*x**m + y(x))/y(x) + Derivative(y(x), x) cannot be solved by the factorable group method