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

Internal problem ID [5818]
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 : Monday, January 27, 2025 at 01:19:57 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 9

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

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 18

DSolve[(y[x])-(3*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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