32.4.6 problem Recognizable Exact Differential equations. Integrating factors. Example 10.781, page 90

Internal problem ID [5817]
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 10.781, page 90
Date solved : Sunday, March 30, 2025 at 10:18:40 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 9

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

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

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 16

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

\begin{align*} y(x)\to c_1 x^3 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 7

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

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