50.21.5 problem 3

Internal problem ID [8142]
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 4.6. Gauss Hypergeometric Equation. Page 187
Problem number : 3
Date solved : Sunday, March 30, 2025 at 12:46:33 PM
CAS classification : [_Gegenbauer, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 1 \end{align*}

✓ Maple. Time used: 0.056 (sec). Leaf size: 338

Order:=8; 
ode:=(-x^2+1)*diff(diff(y(x),x),x)-x*diff(y(x),x)+p^2*y(x) = 0; 
dsolve(ode,y(x),type='series',x=1);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 5699

ode=(1-x^2)*D[y[x],{x,2}]-x*D[y[x],x]+p^2*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,1,7}]
 

Too large to display

✓ Sympy. Time used: 52.747 (sec). Leaf size: 4019

from sympy import * 
x = symbols("x") 
p = symbols("p") 
y = Function("y") 
ode = Eq(p**2*y(x) - x*Derivative(y(x), x) + (1 - x**2)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=1,n=8)
 

\[ \text {Latex too large} \]