56.5.9 problem 9

Internal problem ID [8970]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 9
Date solved : Monday, January 27, 2025 at 05:25:36 PM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 9

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

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