74.10.38 problem 40 (a)

Internal problem ID [16243]
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 (a)
Date solved : Tuesday, January 28, 2025 at 08:58:29 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

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

\[ y = c_{1} {\mathrm e}^{\left (-3+\sqrt {7}\right ) t}+c_{2} {\mathrm e}^{-\left (3+\sqrt {7}\right ) t} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 34

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

\[ y(t)\to e^{-\left (\left (3+\sqrt {7}\right ) t\right )} \left (c_2 e^{2 \sqrt {7} t}+c_1\right ) \]