74.20.4 problem 4

Internal problem ID [16636]
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 : 4
Date solved : Tuesday, January 28, 2025 at 09:13:42 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 x^{\prime \prime }+2 x^{\prime }+8 x&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.052 (sec). Leaf size: 20

dsolve([4*diff(x(t),t$2)+2*diff(x(t),t)+8*x(t)=0,x(0) = 0, D(x)(0) = 2],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {8 \sqrt {31}\, {\mathrm e}^{-\frac {t}{4}} \sin \left (\frac {\sqrt {31}\, t}{4}\right )}{31} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 30

DSolve[{4*D[x[t],{t,2}]+2*D[x[t],t]+8*x[t]==0,{x[0]==0,Derivative[1][x][0 ]==2}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {8 e^{-t/4} \sin \left (\frac {\sqrt {31} t}{4}\right )}{\sqrt {31}} \]