48.2.2 problem Example 3.18

Internal problem ID [7518]
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 : Monday, January 27, 2025 at 03:04:16 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*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 13

dsolve([diff(s(t),t$2)+2*diff(s(t),t)+s(t)=0,s(0) = 4, D(s)(0) = -2],s(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 15

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

\[ s(t)\to 2 e^{-t} (t+2) \]