Internal problem ID [5395]
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]
Solve \begin {gather*} \boxed {y^{2} x -x^{2} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 14
dsolve(x*y(x)^2-diff(y(x),x)*x^2=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {1}{\ln \relax (x )-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.112 (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*}