Internal problem ID [11506]
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).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {x^{\prime \prime \prime }-8 x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(x(t),t$3)-8*x(t)=0,x(t), singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{2 t}+c_{2} {\mathrm e}^{-t} \sin \left (\sqrt {3}\, t \right )+c_{3} {\mathrm e}^{-t} \cos \left (\sqrt {3}\, t \right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 52
DSolve[x'''[t]-x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{-t/2} \left (c_1 e^{3 t/2}+c_2 \cos \left (\frac {\sqrt {3} t}{2}\right )+c_3 \sin \left (\frac {\sqrt {3} t}{2}\right )\right ) \]