74.9.15 problem 26

Internal problem ID [16191]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 08:56:53 AM
CAS classification : [[_2nd_order, _missing_x]]

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

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{-2 t} \end{align*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 22

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

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