78.17.3 problem 2 (a)

Internal problem ID [18409]
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 (a)
Date solved : Tuesday, January 28, 2025 at 11:49:34 AM
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: 0.011 (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: 0.001 (sec). Leaf size: 7

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

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