57.1.4 problem 4

Internal problem ID [14309]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.1 First order equations. Exercises page 10
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:30:33 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ x = {\mathrm e}^{-t} \left (c_1 \sin \left (t \right )+c_2 \cos \left (t \right )\right ) \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 22

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

\begin{align*} x(t)&\to e^{-t} (c_2 \cos (t)+c_1 \sin (t)) \end{align*}

✓ Sympy. Time used: 0.085 (sec). Leaf size: 15

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

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