63.14.3 problem 1(c)

Internal problem ID [13179]
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(c)
Date solved : Tuesday, January 28, 2025 at 05:12:02 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(diff(x(t),t$3)+diff(x(t),t$2)=0,x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 20

DSolve[D[x[t],{t,3}]+D[x[t],{t,2}]==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to c_1 e^{-t}+c_3 t+c_2 \]