74.13.29 problem 46

Internal problem ID [16316]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 46
Date solved : Thursday, March 13, 2025 at 08:10:20 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-16 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ y^{\prime \prime }\left (0\right )&=4\\ y^{\prime \prime \prime }\left (0\right )&=-24 \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 15

ode:=diff(diff(diff(diff(y(t),t),t),t),t)-16*y(t) = 0; 
ic:=y(0) = 1, D(y)(0) = 2, (D@@2)(y)(0) = 4, (D@@3)(y)(0) = -24; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = {\mathrm e}^{-2 t}+2 \sin \left (2 t \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 17

ode=D[y[t],{t,4}]-16*y[t]==0; 
ic={y[0]==1,Derivative[1][y][0] ==2,Derivative[2][y][0] ==4,Derivative[3][y][0]==-24}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-2 t}+2 \sin (2 t) \]

✓ Sympy. Time used: 0.147 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-16*y(t) + Derivative(y(t), (t, 4)),0) 
ics = {y(0): 1, Subs(Derivative(y(t), t), t, 0): 2, Subs(Derivative(y(t), (t, 2)), t, 0): 4, Subs(Derivative(y(t), (t, 3)), t, 0): -24} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 2 \sin {\left (2 t \right )} + e^{- 2 t} \]