14.15.5 problem 5

Internal problem ID [2670]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.8.3, Equal roots and roots differing by an integer. Excercises page 223
Problem number : 5
Date solved : Tuesday, March 04, 2025 at 02:33:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.143 (sec). Leaf size: 8537

Order:=6; 
ode:=t^2*diff(diff(y(t),t),t)+t*p(t)*diff(y(t),t)+q(t)*y(t) = 0; 
dsolve(ode,y(t),type='series',t=0);
 

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 11270

ode=t^2*D[y[t],{t,2}]+t*p[t]*D[y[t],t]+q[t]*y[t]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[t],{t,0,5}]
 

Too large to display

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) + t*p(t)*Derivative(y(t), t) + q(t)*y(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