74.10.40 problem 40 (c)

Internal problem ID [16245]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 40 (c)
Date solved : Tuesday, January 28, 2025 at 08:58:32 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }-16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(t),t$2)-6*diff(y(t),t)-16*y(t)=0,y(t), singsol=all)
 

\[ y = {\mathrm e}^{8 t} c_{1} +{\mathrm e}^{-2 t} c_{2} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 22

DSolve[D[y[t],{t,2}]-6*D[y[t],t]-16*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_1 e^{-2 t}+c_2 e^{8 t} \]