37.1.4 problem 10.2.8 part(2)

Internal problem ID [6391]
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)
Date solved : Monday, January 27, 2025 at 01:58:46 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 61

dsolve(diff(x(t),t$4)+x(t)=0,x(t), singsol=all)
 

\[ x \left (t \right ) = \left (-c_1 \,{\mathrm e}^{-\frac {\sqrt {2}\, t}{2}}-c_2 \,{\mathrm e}^{\frac {\sqrt {2}\, t}{2}}\right ) \sin \left (\frac {\sqrt {2}\, t}{2}\right )+\left (c_3 \,{\mathrm e}^{-\frac {\sqrt {2}\, t}{2}}+c_4 \,{\mathrm e}^{\frac {\sqrt {2}\, t}{2}}\right ) \cos \left (\frac {\sqrt {2}\, t}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 65

DSolve[D[x[t],{t,4}]+x[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-\frac {t}{\sqrt {2}}} \left (\left (c_1 e^{\sqrt {2} t}+c_2\right ) \cos \left (\frac {t}{\sqrt {2}}\right )+\left (c_4 e^{\sqrt {2} t}+c_3\right ) \sin \left (\frac {t}{\sqrt {2}}\right )\right ) \]