76.24.11 problem 13

Internal problem ID [17810]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 6. Systems of First Order Linear Equations. Section 6.2 (Basic Theory of First Order Linear Systems). Problems at page 398
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 11:03:18 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }-4 y^{\prime }-16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(diff(y(t),t$3)+4*diff(y(t),t$2)-4*diff(y(t),t)-16*y(t)=0,y(t), singsol=all)
 

\[ y = \left (c_{2} {\mathrm e}^{6 t}+c_{3} {\mathrm e}^{2 t}+c_{1} \right ) {\mathrm e}^{-4 t} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[D[y[t],{t,3}]+4*D[y[t],{t,2}]-4*D[y[t],t]-16*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t} \left (c_2 e^{2 t}+c_3 e^{6 t}+c_1\right ) \]