74.10.7 problem 7

Internal problem ID [16212]
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 : 7
Date solved : Tuesday, January 28, 2025 at 08:57:19 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 8 y^{\prime \prime }+6 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(8*diff(y(t),t$2)+6*diff(y(t),t)+y(t)=0,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 26

DSolve[8*D[y[t],{t,2}]+6*D[y[t],t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

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