Internal problem ID [4540]
Book: Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section: Chapter 10, Differential equations. Section 10.2, ODEs with constant Coefficients. page
307
Problem number: 10.2.8 part(2).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {x^{\prime \prime \prime \prime }+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 71
dsolve(diff(x(t),t$4)+x(t)=0,x(t), singsol=all)
\[ x \relax (t ) = -c_{1} {\mathrm e}^{-\frac {\sqrt {2}\, t}{2}} \sin \left (\frac {\sqrt {2}\, t}{2}\right )-c_{2} {\mathrm e}^{\frac {\sqrt {2}\, t}{2}} \sin \left (\frac {\sqrt {2}\, t}{2}\right )+c_{3} {\mathrm e}^{-\frac {\sqrt {2}\, t}{2}} \cos \left (\frac {\sqrt {2}\, t}{2}\right )+c_{4} {\mathrm e}^{\frac {\sqrt {2}\, t}{2}} \cos \left (\frac {\sqrt {2}\, t}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 65
DSolve[x''''[t]+x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-\frac {t}{\sqrt {2}}} \left (\left (c_1 e^{\sqrt {2} t}+c_2\right ) \cos \left (\frac {t}{\sqrt {2}}\right )+\left (c_4 e^{\sqrt {2} t}+c_3\right ) \sin \left (\frac {t}{\sqrt {2}}\right )\right ) \\ \end{align*}