74.10.41 problem 40 (d)

Internal problem ID [16246]
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 (d)
Date solved : Tuesday, January 28, 2025 at 08:58:34 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

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

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

\[ y = {\mathrm e}^{-4 t} c_{1} +c_{2} {\mathrm e}^{4 t} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 22

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

\[ y(t)\to e^{-4 t} \left (c_1 e^{8 t}+c_2\right ) \]