74.13.25 problem 42

Internal problem ID [16391]
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 : 42
Date solved : Tuesday, January 28, 2025 at 09:07:26 AM
CAS classification : [[_high_order, _missing_x]]

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

With initial conditions

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

Solution by Maple

Time used: 0.023 (sec). Leaf size: 20

dsolve([diff(y(t),t$4)+16*diff(y(t),t$3)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 1],y(t), singsol=all)
 
\[ y = \frac {1}{4096}+\frac {255 t}{256}+\frac {t^{2}}{32}-\frac {{\mathrm e}^{-16 t}}{4096} \]

Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 26

DSolve[{D[y[t],{t,4}]+16*D[ y[t],{t,3}]==0,{y[0]==0,Derivative[1][y][0] ==1,Derivative[2][y][0] ==0,Derivative[3][y][0]==1}},y[t],t,IncludeSingularSolutions -> True]
 
\[ y(t)\to \frac {128 t^2+4080 t-e^{-16 t}+1}{4096} \]