29.9.13 problem 7, using series method

Internal problem ID [7383]
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
Date solved : Tuesday, September 30, 2025 at 04:30:08 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 25

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

\[ y = c_1 \,x^{3} \left (1+\operatorname {O}\left (x^{6}\right )\right )+c_2 x \left (-2+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 14

ode=x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+3*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

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

✓ Sympy. Time used: 0.203 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 3*x*Derivative(y(x), x) + 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

\[ y{\left (x \right )} = C_{2} x^{3} + C_{1} x + O\left (x^{6}\right ) \]