89.11.11 problem 11

Internal problem ID [24536]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 117
Problem number : 11
Date solved : Thursday, October 02, 2025 at 10:45:58 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime }-2 x^{\prime \prime }-3 x^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=diff(diff(diff(x(t),t),t),t)-2*diff(diff(x(t),t),t)-3*diff(x(t),t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 +c_2 \,{\mathrm e}^{3 t}+c_3 \,{\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 28

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

\begin{align*} x(t)&\to c_1 \left (-e^{-t}\right )+\frac {1}{3} c_2 e^{3 t}+c_3 \end{align*}

✓ Sympy. Time used: 0.091 (sec). Leaf size: 15

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

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