63.14.2 problem 1(b)

Internal problem ID [13107]
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(b)
Date solved : Monday, March 31, 2025 at 07:34:29 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime }+x^{\prime }&=1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=diff(diff(diff(x(t),t),t),t)+diff(x(t),t) = 1; 
dsolve(ode,x(t), singsol=all);
 

\[ x = \sin \left (t \right ) c_1 -\cos \left (t \right ) c_2 +t +c_3 \]

✓ Mathematica. Time used: 60.01 (sec). Leaf size: 29

ode=D[x[t],{t,3}]+D[x[t],t]==1; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to \int _1^t(c_1 \cos (K[1])+c_2 \sin (K[1])+1)dK[1]+c_3 \]

✓ Sympy. Time used: 0.133 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(Derivative(x(t), t) + Derivative(x(t), (t, 3)) - 1,0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} + C_{2} \sin {\left (t \right )} + C_{3} \cos {\left (t \right )} + t \]