Internal problem ID [10488]
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: 0.003 (sec). Leaf size: 49
DSolve[x'''[t]-x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^t+e^{-t/2} \left (c_2 \cos \left (\frac {\sqrt {3} t}{2}\right )+c_3 \sin \left (\frac {\sqrt {3} t}{2}\right )\right ) \\ \end{align*}