Internal problem ID [5666]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of
First-Order Differential Equations Page 162
Problem number: 2(b) solving directly.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(x^2*diff(y(x),x)=y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {1}{x}} \]
✓ Solution by Mathematica
Time used: 0.021 (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*}