74.18.48 problem 54 (b)

Internal problem ID [16534]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 54 (b)
Date solved : Monday, March 31, 2025 at 02:55:47 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \end{align*}

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

ode:=diff(diff(y(t),t),t)+4*diff(y(t),t)+4*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 18

ode=D[y[t],{t,2}]+4*D[y[t],t]+4*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.156 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) + 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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