Internal problem ID [5665]
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 using series.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=8; dsolve(x^2*diff(y(x),x)=y(x),y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 13
AsymptoticDSolveValue[x^2*y'[x]==y[x],y[x],{x,0,7}]
\[ y(x)\to c_1 e^{-1/x} \]