73.2.7 problem 5 (iv)

Internal problem ID [19806]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 4. Autonomous systems. Exercises at page 69
Problem number : 5 (iv)
Date solved : Thursday, October 02, 2025 at 04:43:59 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 19

ode=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_2-\frac {1}{3} c_1 e^{-3 t} \end{align*}

✓ Sympy. Time used: 0.077 (sec). Leaf size: 10

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

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