74.9.12 problem 22

Internal problem ID [16188]
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 : 22
Date solved : Tuesday, January 28, 2025 at 08:56:49 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+18 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(diff(y(t),t$2)+6*diff(y(t),t)+18*y(t)=0,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 26

DSolve[D[y[t],{t,2}]+6*D[y[t],t]+18*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

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