35.9.5 problem 3, using series method

Internal problem ID [6240]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page 564
Problem number : 3, using series method
Date solved : Monday, January 27, 2025 at 01:49:50 PM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 12

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

\[ y = c_{1} x +O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 7

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

\[ y(x)\to c_1 x \]