74.13.11 problem 28

Internal problem ID [16377]
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 : 28
Date solved : Tuesday, January 28, 2025 at 09:07:20 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-9 y^{\prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 21

dsolve(diff(y(t),t$4)-9*diff(y(t),t$2)=0,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 32

DSolve[D[y[t],{t,4}]-9*D[y[t],{t,2}]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{9} e^{-3 t} \left (c_1 e^{6 t}+c_2\right )+c_4 t+c_3 \]