9.7.18 problem problem 18

Internal problem ID [1059]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Chapter 11 Power series methods. Section 11.1 Introduction and Review of power series. Page 615
Problem number : problem 18
Date solved : Monday, January 27, 2025 at 04:32:40 AM
CAS classification : [_separable]

\begin{align*} x^{3} y^{\prime }&=2 y \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✗ Solution by Maple

Order:=6; 
dsolve(x^3*diff(y(x),x)=2*y(x),y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 13

AsymptoticDSolveValue[x^3*D[y[x],x]==2*y[x],y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 e^{-\frac {1}{x^2}} \]