37.1.5 problem 10.2.8 part(3)

Internal problem ID [6392]
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(3)
Date solved : Wednesday, March 05, 2025 at 12:37:23 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=diff(diff(diff(x(t),t),t),t)-3*diff(diff(x(t),t),t)-9*diff(x(t),t)-5*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x \left (t \right ) = \left (t c_3 +c_2 \right ) {\mathrm e}^{-t}+c_1 \,{\mathrm e}^{5 t} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 26

ode=D[x[t],{t,3}]-3*D[x[t],{t,2}]-9*D[x[t],t]-5*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to e^{-t} \left (c_2 t+c_3 e^{6 t}+c_1\right ) \]

✓ Sympy. Time used: 0.176 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-5*x(t) - 9*Derivative(x(t), t) - 3*Derivative(x(t), (t, 2)) + Derivative(x(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{3} e^{5 t} + \left (C_{1} + C_{2} t\right ) e^{- t} \]