63.14.6 problem 1(f)

Internal problem ID [13182]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.5 Higher order equations. Exercises page 130
Problem number : 1(f)
Date solved : Tuesday, January 28, 2025 at 05:12:03 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime }-8 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 35

dsolve(diff(x(t),t$3)-8*x(t)=0,x(t), singsol=all)
 

\[ x \left (t \right ) = c_{1} {\mathrm e}^{2 t}+{\mathrm e}^{-t} \sin \left (\sqrt {3}\, t \right ) c_{2} +c_{3} {\mathrm e}^{-t} \cos \left (\sqrt {3}\, t \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 52

DSolve[D[x[t],{t,3}]-x[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-t/2} \left (c_1 e^{3 t/2}+c_2 \cos \left (\frac {\sqrt {3} t}{2}\right )+c_3 \sin \left (\frac {\sqrt {3} t}{2}\right )\right ) \]