74.20.1 problem 1

Internal problem ID [16562]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 5. Applications of Higher Order Equations. Exercises 5.2, page 241
Problem number : 1
Date solved : Monday, March 31, 2025 at 02:58:49 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=-4 \end{align*}

✓ Maple. Time used: 0.049 (sec). Leaf size: 17

ode:=diff(diff(x(t),t),t)+4*diff(x(t),t)+3*x(t) = 0; 
ic:=x(0) = 0, D(x)(0) = -4; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x = -2 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{-3 t} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 19

ode=D[x[t],{t,2}]+4*D[x[t],t]+3*x[t]==0; 
ic={x[0]==0,Derivative[1][x][0 ]==-4}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to -2 e^{-3 t} \left (e^{2 t}-1\right ) \]

✓ Sympy. Time used: 0.177 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(3*x(t) + 4*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {x(0): 0, Subs(Derivative(x(t), t), t, 0): -4} 
dsolve(ode,func=x(t),ics=ics)
 

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