Internal problem ID [5663]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of
First-Order Differential Equations Page 162
Problem number: 2(a) solving using series.
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: 0.078 (sec). Leaf size: 13
Order:=8; dsolve(x*diff(y(x),x)=y(x),y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x +O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 7
AsymptoticDSolveValue[x*y'[x]==y[x],y[x],{x,0,7}]
\[ y(x)\to c_1 x \]