9.13 problem 7, using series method

Internal problem ID [4396]

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: 7, using series method.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_Emden, _Fowler]]

Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).

Solution by Maple

Time used: 0.079 (sec). Leaf size: 25

Order:=6; 
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+3*y(x)=0,y(x),type='series',x=0);
 

\[ y \relax (x ) = c_{1} x^{3} \left (1+\mathrm {O}\left (x^{6}\right )\right )+c_{2} x \left (-2+\mathrm {O}\left (x^{6}\right )\right ) \]

Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 14

AsymptoticDSolveValue[x^2*y''[x]-3*x*y'[x]+3*y[x]==0,y[x],{x,0,5}]
 

\[ y(x)\to c_2 x^3+c_1 x \]