74.13.15 problem 32

Internal problem ID [16381]
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 : 32
Date solved : Tuesday, January 28, 2025 at 09:07:21 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

dsolve(diff(y(t),t$4)+2*diff(y(t),t$3)-2*diff(y(t),t$2)+8*y(t)=0,y(t), singsol=all)
 

\[ y = \left (c_{3} {\mathrm e}^{3 t} \sin \left (t \right )+c_4 \,{\mathrm e}^{3 t} \cos \left (t \right )+c_{2} t +c_{1} \right ) {\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 38

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

\[ y(t)\to e^{-2 t} \left (c_4 t+c_2 e^{3 t} \cos (t)+c_1 e^{3 t} \sin (t)+c_3\right ) \]