26.4.7 problem Recognizable Exact Differential equations. Integrating factors. Example 10.81, page 90

Internal problem ID [6953]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number : Recognizable Exact Differential equations. Integrating factors. Example 10.81, page 90
Date solved : Tuesday, September 30, 2025 at 04:07:12 PM
CAS classification : [_separable]

\begin{align*} y-3 x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

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

\[ y = c_1 \,x^{{1}/{3}} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to c_1 \sqrt [3]{x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.066 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = C_{1} \sqrt [3]{x} \]