14.14.26 problem 26

Internal problem ID [2663]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.8.2, Regular singular points, the method of Frobenius. Excercises page 216
Problem number : 26
Date solved : Tuesday, March 04, 2025 at 02:33:19 PM
CAS classification : [_Jacobi]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 447

Order:=6; 
ode:=t*(1-t)*diff(diff(y(t),t),t)+(gamma-(1+alpha+beta)*t)*diff(y(t),t)-alpha*beta*y(t) = 0; 
dsolve(ode,y(t),type='series',t=0);
 

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 2342

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

Too large to display

✗ Sympy

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

ValueError : Expected Expr or iterable but got None