50.17.16 problem 2(b) solving directly

Internal problem ID [8087]
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
Date solved : Monday, January 27, 2025 at 03:43:28 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 12

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

\[ y = c_{1} {\mathrm e}^{-\frac {1}{x}} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 20

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

\begin{align*} y(x)\to c_1 e^{-1/x} \\ y(x)\to 0 \\ \end{align*}