74.22.14 problem 14

Internal problem ID [16661]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 09:16:25 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+6 x^{\prime }+9 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(diff(x(t),t$2)+6*diff(x(t),t)+9*x(t)=0,x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 18

DSolve[D[x[t],{t,2}]+6*D[x[t],t]+9*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-3 t} (c_2 t+c_1) \]