Internal problem ID [4896]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-y+x y^{\prime }=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
Order:=6; dsolve(x*diff(y(x),x)=y(x),y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x +O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 7
AsymptoticDSolveValue[x*y'[x]==y[x],y[x],{x,0,5}]
\[ y(x)\to c_1 x \]