Internal problem ID [6251]
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. Problems for Review and Discovery. Page
53
Problem number: 1(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{2} y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(x^2*diff(y(x),x)=y(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {1}{x}} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 20
DSolve[x^2*y'[x]==y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-1/x} y(x)\to 0 \end{align*}