74.20.1 problem 1

Internal problem ID [16633]
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 : Tuesday, January 28, 2025 at 09:13:36 AM
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*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 17

dsolve([diff(x(t),t$2)+4*diff(x(t),t)+3*x(t)=0,x(0) = 0, D(x)(0) = -4],x(t), singsol=all)
 

\[ x \left (t \right ) = 2 \,{\mathrm e}^{-3 t}-2 \,{\mathrm e}^{-t} \]

✓ Solution by Mathematica

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

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

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