89.11.12 problem 12

Internal problem ID [24537]
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 : 12
Date solved : Thursday, October 02, 2025 at 10:45:58 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime }-7 x^{\prime }+6 x&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(diff(diff(x(t),t),t),t)-7*diff(x(t),t)+6*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = \left (c_1 \,{\mathrm e}^{5 t}+c_3 \,{\mathrm e}^{4 t}+c_2 \right ) {\mathrm e}^{-3 t} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 28

ode=D[x[t],{t,3}] - 7*D[x[t],t] +6*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to c_1 e^{-3 t}+c_2 e^t+c_3 e^{2 t} \end{align*}

✓ Sympy. Time used: 0.090 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(6*x(t) - 7*Derivative(x(t), t) + Derivative(x(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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