79.2.5 problem 5 (ii)

Internal problem ID [18439]
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 (ii)
Date solved : Thursday, March 13, 2025 at 11:57:09 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-4 x^{\prime }+4 x&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

ode:=diff(diff(x(t),t),t)-4*diff(x(t),t)+4*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = {\mathrm e}^{2 t} \left (c_{2} t +c_{1} \right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 18

ode=D[x[t],{t,2}]-4*D[x[t],t]+4*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to e^{2 t} (c_2 t+c_1) \]

✓ Sympy. Time used: 0.157 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(4*x(t) - 4*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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