68.10.38 problem 40 (a)

Internal problem ID [17530]
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 : Thursday, October 02, 2025 at 02:25:08 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

ode:=diff(diff(y(t),t),t)+6*diff(y(t),t)+2*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 34

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

\begin{align*} y(t)&\to e^{-\left (\left (3+\sqrt {7}\right ) t\right )} \left (c_2 e^{2 \sqrt {7} t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 26

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

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