74.13.29 problem 46

Internal problem ID [16395]
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 : Tuesday, January 28, 2025 at 09:07:27 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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