50.19.13 problem 3(d)

Internal problem ID [8121]
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 4.4. REGULAR SINGULAR POINTS. Page 175
Problem number : 3(d)
Date solved : Sunday, March 30, 2025 at 12:45:58 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 x y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.033 (sec). Leaf size: 32

Order:=8; 
ode:=x^3*diff(diff(y(x),x),x)-4*x^2*diff(y(x),x)+3*x*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = x^{{5}/{2}} \left (x^{-\frac {\sqrt {13}}{2}} c_1 +x^{\frac {\sqrt {13}}{2}} c_2 \right )+O\left (x^{8}\right ) \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 38

ode=x^3*D[y[x],{x,2}]-4*x^2*D[y[x],x]+3*x*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,7}]
 

\[ y(x)\to c_1 x^{\frac {1}{2} \left (5+\sqrt {13}\right )}+c_2 x^{\frac {1}{2} \left (5-\sqrt {13}\right )} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 2)) - 4*x**2*Derivative(y(x), x) + 3*x*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=8)
 

NotImplementedError : Not sure of sign of 11/2 - x0