Internal problem ID [6549]
Book: Own collection of miscellaneous problems
Section: section 5.0
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 15
Order:=6; dsolve(x*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1}}{x}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 9
AsymptoticDSolveValue[x*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to \frac {c_1}{x} \]