80.5.16 problem B 16

Internal problem ID [21237]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 5. Second order equations. Excercise 5.9 at page 119
Problem number : B 16
Date solved : Thursday, October 02, 2025 at 07:27:11 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-2 x^{\prime }+2 x&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=diff(diff(x(t),t),t)-2*diff(x(t),t)+2*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.081 (sec). Leaf size: 15

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

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