74.13.16 problem 33

Internal problem ID [16382]
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 : 33
Date solved : Tuesday, January 28, 2025 at 09:07:22 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

dsolve(diff(y(t),t$5)+4*diff(y(t),t$4)=0,y(t), singsol=all)
 

\[ y = c_{1} +c_{2} t +t^{2} c_{3} +c_4 \,t^{3}+c_5 \,{\mathrm e}^{-4 t} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 33

DSolve[D[ y[t],{t,5}]+4*D[y[t],{t,4}]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{256} c_1 e^{-4 t}+t (t (c_5 t+c_4)+c_3)+c_2 \]