9.1 problem 1, using series method

Internal problem ID [4384]

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: 1, using series method.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {y^{\prime } x -y x -y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).

Solution by Maple

Time used: 0.047 (sec). Leaf size: 23

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

\[ y \relax (x ) = c_{1} x \left (1+x +\frac {1}{2} x^{2}+\frac {1}{6} x^{3}+\frac {1}{24} x^{4}+\frac {1}{120} x^{5}\right )+O\left (x^{6}\right ) \]

Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 38

AsymptoticDSolveValue[x*y'[x]==x*y[x]+y[x],y[x],{x,0,5}]
 

\[ y(x)\to c_1 x \left (\frac {x^5}{120}+\frac {x^4}{24}+\frac {x^3}{6}+\frac {x^2}{2}+x+1\right ) \]