74.10.7 problem 7

Internal problem ID [16133]
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 : 7
Date solved : Thursday, March 13, 2025 at 07:52:36 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 8 y^{\prime \prime }+6 y^{\prime }+y&=0 \end{align*}

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

ode:=8*diff(diff(y(t),t),t)+6*diff(y(t),t)+y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_{1} {\mathrm e}^{-\frac {t}{4}}+c_{2} {\mathrm e}^{-\frac {t}{2}} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 26

ode=8*D[y[t],{t,2}]+6*D[y[t],t]+y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-t/2} \left (c_1 e^{t/4}+c_2\right ) \]

✓ Sympy. Time used: 0.152 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) + 6*Derivative(y(t), t) + 8*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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