78.17.4 problem 2 (b)

Internal problem ID [18410]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 5. Power Series Solutions and Special Functions. Section 27. Series Solutions of First Order Equations. Problems at page 208
Problem number : 2 (b)
Date solved : Tuesday, January 28, 2025 at 11:49:35 AM
CAS classification : [_separable]

\begin{align*} x^{2} y^{\prime }&=y \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),y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 13

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

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