74.10.5 problem 5

Internal problem ID [16131]
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 : 5
Date solved : Thursday, March 13, 2025 at 07:52:33 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+12 y&=0 \end{align*}

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

ode:=diff(diff(y(t),t),t)+8*diff(y(t),t)+12*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_{1} {\mathrm e}^{-6 t}+{\mathrm e}^{-2 t} c_{2} \]

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

ode=D[y[t],{t,2}]+8*D[y[t],t]+12*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-6 t} \left (c_2 e^{4 t}+c_1\right ) \]

✓ Sympy. Time used: 0.185 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(12*y(t) + 8*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} + C_{2} e^{- 4 t}\right ) e^{- 2 t} \]