63.14.3 problem 1(c)

Internal problem ID [13100]
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 : Wednesday, March 05, 2025 at 09:17:21 PM
CAS classification : [[_3rd_order, _missing_x]]

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

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

ode:=diff(diff(diff(x(t),t),t),t)+diff(diff(x(t),t),t) = 0; 
dsolve(ode,x(t), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.083 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(Derivative(x(t), (t, 2)) + Derivative(x(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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