30.12.5 problem 5

Internal problem ID [7597]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 4, Linear Second-Order Equations. EXERCISES 4.2 at page 164
Problem number : 5
Date solved : Tuesday, September 30, 2025 at 04:54:46 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=diff(diff(y(t),t),t)+8*diff(y(t),t)+16*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 18

ode=D[y[t],{t,2}]+8*D[y[t],t]+16*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-4 t} (c_2 t+c_1) \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(16*y(t) + 8*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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