74.12.57 problem 63 (c)

Internal problem ID [16293]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 63 (c)
Date solved : Monday, March 31, 2025 at 02:49:46 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y&=16 t^{{3}/{2}} \end{align*}

With initial conditions

\begin{align*} y \left (\pi \right )&=0\\ y^{\prime }\left (2 \pi \right )&=0 \end{align*}

✓ Maple. Time used: 0.069 (sec). Leaf size: 15

ode:=4*t^2*diff(diff(y(t),t),t)+4*t*diff(y(t),t)+(16*t^2-1)*y(t) = 16*t^(3/2); 
ic:=y(Pi) = 0, D(y)(2*Pi) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = -\frac {\cos \left (2 t \right )-1}{\sqrt {t}} \]

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 32

ode=4*t^2*D[y[t],{t,2}]+4*t*D[y[t],t]+(16*t^2-1)*y[t]==16*t^(3/2); 
ic={y[Pi]==0,Derivative[1][y][2*Pi]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -\frac {e^{-2 i t} \left (-1+e^{2 i t}\right )^2}{2 \sqrt {t}} \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-16*t**(3/2) + 4*t**2*Derivative(y(t), (t, 2)) + 4*t*Derivative(y(t), t) + (16*t**2 - 1)*y(t),0) 
ics = {y(pi): 0, Subs(Derivative(y(t), t), t, 2*pi): 0} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE -4*sqrt(t) + 4*t*y(t) + t*Derivative(y(t), (t, 2)) + Derivative(y(t), t) - y(t)/(4*t) cannot be solved by the factorable group method