7.15.41 problem 42

Internal problem ID [497]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.3 (Regular singular points). Problems at page 231
Problem number : 42
Date solved : Thursday, March 13, 2025 at 03:36:03 PM
CAS classification : [_Jacobi]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 447

Order:=6; 
ode:=x*(1-x)*diff(diff(y(x),x),x)+(gamma-(alpha+beta+1)*x)*diff(y(x),x)-alpha*beta*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

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

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 2568

ode=x*(1-x)*D[y[x],{x,2}]+(\[Gamma]-(\[Alpha]+\[Beta]+1)*x)*D[y[x],x]-\[Alpha]*\[Beta]*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
Alpha = symbols("Alpha") 
BETA = symbols("BETA") 
Gamma = symbols("Gamma") 
y = Function("y") 
ode = Eq(-Alpha*BETA*y(x) + x*(1 - x)*Derivative(y(x), (x, 2)) + (Gamma - x*(Alpha + BETA + 1))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

ValueError : Expected Expr or iterable but got None