7.13.17 problem 17

Internal problem ID [416]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.1 (Introduction). Problems at page 206
Problem number : 17
Date solved : Monday, January 27, 2025 at 02:53:30 AM
CAS classification : [_separable]

\begin{align*} x^{2} y^{\prime }+y&=0 \end{align*}

Using series method with expansion around

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 11

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

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