Internal problem ID [5097]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {s^{\prime \prime }+2 s^{\prime }+s=0} \end {gather*} With initial conditions \begin {align*} [s \relax (0) = 4, s^{\prime }\relax (0) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.01 (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)
\[ s \relax (t ) = 2 \left (t +2\right ) {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 15
DSolve[{s''[t]+2*s'[t]+s[t]==0,{s[0]==4,s'[0]==-2}},s[t],t,IncludeSingularSolutions -> True]
\begin{align*} s(t)\to 2 e^{-t} (t+2) \\ \end{align*}