78.2.4 problem 1.d

Internal problem ID [20956]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 2, Second order ODEs. Problems section 2.6
Problem number : 1.d
Date solved : Thursday, October 02, 2025 at 07:00:40 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

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

\[ x = \left (c_2 \,{\mathrm e}^{5 t}+c_1 \right ) {\mathrm e}^{-2 t} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 22

ode=D[x[t],{t,2}]-D[x[t],t]-6*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to e^{-2 t} \left (c_2 e^{5 t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.085 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-6*x(t) - Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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