73.2.6 problem 5 (iiI=i)

Internal problem ID [19805]
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 (iiI=i)
Date solved : Thursday, October 02, 2025 at 04:43:59 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-4 x^{\prime }+5 x&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=diff(diff(x(t),t),t)-4*diff(x(t),t)+5*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = {\mathrm e}^{2 t} \left (c_1 \sin \left (t \right )+c_2 \cos \left (t \right )\right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 22

ode=D[x[t],{t,2}]-4*D[x[t],t]+5*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to e^{2 t} (c_2 \cos (t)+c_1 \sin (t)) \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(5*x(t) - 4*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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