60.1.47 problem 47

Internal problem ID [10061]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 47
Date solved : Wednesday, March 05, 2025 at 08:09:14 AM
CAS classification : [_Abel]

\begin{align*} y^{\prime }-a \left (x^{n}-x \right ) y^{3}-y^{2}&=0 \end{align*}

✗ Maple

ode:=diff(y(x),x)-a*(x^n-x)*y(x)^3-y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x] - a*(x^n - x)*y[x]^3 - y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
n = symbols("n") 
y = Function("y") 
ode = Eq(-a*(-x + x**n)*y(x)**3 - y(x)**2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(-a*x*y(x) + a*x**n*y(x) + 1)*y(x)**2 + Derivative(y(x), x) cannot be solved by the factorable group method