74.20.2 problem 2

Internal problem ID [16634]
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 : 2
Date solved : Tuesday, January 28, 2025 at 09:13:38 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} \frac {x^{\prime \prime }}{32}+2 x^{\prime }+x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.079 (sec). Leaf size: 41

dsolve([1/32*diff(x(t),t$2)+2*diff(x(t),t)+x(t)=0,x(0) = 1, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\left (31+4 \sqrt {62}\right ) {\mathrm e}^{4 \left (-8+\sqrt {62}\right ) t}}{62}+\frac {\left (31-4 \sqrt {62}\right ) {\mathrm e}^{-4 \left (8+\sqrt {62}\right ) t}}{62} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 50

DSolve[{1/32*D[x[t],{t,2}]+2*D[x[t],t]+x[t]==0,{x[0]==1,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{62} e^{-4 \left (8+\sqrt {62}\right ) t} \left (\left (31+4 \sqrt {62}\right ) e^{8 \sqrt {62} t}+31-4 \sqrt {62}\right ) \]