42.2.2 problem Example 3.18

Internal problem ID [8804]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.3 SECOND ORDER ODE. Page 147
Problem number : Example 3.18
Date solved : Tuesday, September 30, 2025 at 05:52:41 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} s \left (0\right )&=4 \\ s^{\prime }\left (0\right )&=-2 \\ \end{align*}

✓ Maple. Time used: 0.043 (sec). Leaf size: 13

ode:=diff(diff(s(t),t),t)+2*diff(s(t),t)+s(t) = 0; 
ic:=[s(0) = 4, D(s)(0) = -2]; 
dsolve([ode,op(ic)],s(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 15

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

\begin{align*} s(t)&\to 2 e^{-t} (t+2) \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 10

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

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