Internal problem ID [5394]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y^{2}-x^{2} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(x*y(x)^2-diff(y(x),x)*x^2=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{\ln \left (x \right )-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.1 (sec). Leaf size: 19
DSolve[x*y[x]^2-y'[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*}