37.1.2 problem 10.2.5

Internal problem ID [6389]
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 : 10.2.5
Date solved : Wednesday, March 05, 2025 at 12:37:20 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 22

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

\[ x(t)\to c_3 e^t+c_1 \cos (t)+c_2 \sin (t) \]

✓ Sympy. Time used: 0.126 (sec). Leaf size: 17

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

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