50.2.10 problem 1(j)

Internal problem ID [7816]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 1(j)
Date solved : Monday, January 27, 2025 at 03:23:58 PM
CAS classification : [_separable]

\begin{align*} x y^{2}-x^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

dsolve(x*y(x)^2-diff(y(x),x)*x^2=0,y(x), singsol=all)
 

\[ y = \frac {1}{-\ln \left (x \right )+c_{1}} \]

✓ Solution by Mathematica

Time used: 0.110 (sec). Leaf size: 19

DSolve[x*y[x]^2-D[y[x],x]*x^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\log (x)+c_1} \\ y(x)\to 0 \\ \end{align*}