74.13.13 problem 30

Internal problem ID [16379]
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 : 30
Date solved : Tuesday, January 28, 2025 at 09:07:21 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }-y^{\prime \prime }+54 y^{\prime }-72 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

dsolve(diff(y(t),t$4)-6*diff(y(t),t$3)-diff(y(t),t$2)+54*diff(y(t),t)-72*y(t)=0,y(t), singsol=all)
 

\[ y = \left (c_4 \,{\mathrm e}^{7 t}+c_{2} {\mathrm e}^{6 t}+c_{3} {\mathrm e}^{5 t}+c_{1} \right ) {\mathrm e}^{-3 t} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 36

DSolve[D[y[t],{t,4}]-6*D[ y[t],{t,3}]-D[y[t],{t,2}]+54*D[y[t],t]-72*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} \left (e^{5 t} \left (e^t \left (c_4 e^t+c_3\right )+c_2\right )+c_1\right ) \]