74.13.32 problem 49

Internal problem ID [16398]
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 : 49
Date solved : Tuesday, January 28, 2025 at 09:07:29 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+8 y^{\prime \prime \prime \prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=4\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=48\\ y^{\prime \prime \prime \prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 14

dsolve([diff(y(t),t$5)+8*diff(y(t),t$4)=0,y(0) = 8, D(y)(0) = 4, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 48, (D@@4)(y)(0) = 0],y(t), singsol=all)
 

\[ y = 8 t^{3}+4 t +8 \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 15

DSolve[{D[ y[t],{t,5}]+8*D[y[t],{t,4}]==0,{y[0]==8,Derivative[1][y][0] ==4,Derivative[2][y][0] ==0,Derivative[3][y][0]==48,Derivative[4][y][0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 4 \left (2 t^3+t+2\right ) \]