60.1.48 problem 48

Internal problem ID [10062]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 48
Date solved : Sunday, March 30, 2025 at 02:58:39 PM
CAS classification : [_Abel]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x] - (a*x^n + b*x)*y[x]^3 - c*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") 
b = symbols("b") 
c = symbols("c") 
n = symbols("n") 
y = Function("y") 
ode = Eq(-c*y(x)**2 - (a*x**n + b*x)*y(x)**3 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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