68.9.12 problem 22

Internal problem ID [17475]
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 : Thursday, October 02, 2025 at 02:24:33 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

ode:=diff(diff(y(t),t),t)+6*diff(y(t),t)+18*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-3 t} \left (c_1 \sin \left (3 t \right )+c_2 \cos \left (3 t \right )\right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 26

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

\begin{align*} y(t)&\to e^{-3 t} (c_2 \cos (3 t)+c_1 \sin (3 t)) \end{align*}

✓ Sympy. Time used: 0.096 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(18*y(t) + 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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