80.5.23 problem B 23

Internal problem ID [21244]
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 23
Date solved : Thursday, October 02, 2025 at 07:27:16 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-2 x^{\prime }+5 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=0 \\ x^{\prime }\left (\theta \right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 5

ode:=diff(diff(x(t),t),t)-2*diff(x(t),t)+5*x(t) = 0; 
ic:=[x(0) = 0, D(x)(theta) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = 0 \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 38

ode=D[x[t],{t,2}]-2*D[x[t],t]+5*x[t]==0; 
ic={x[0]==0,Derivative[1][x][\[Theta]] ==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \begin {array}{cc} \{ & \begin {array}{cc} e^t c_1 \sin (2 t) & e^{\theta }=0\lor 2 \cos (2 \theta )+\sin (2 \theta )=0 \\ 0 & \text {True} \\ \end {array} \\ \end {array} \end{align*}

✓ Sympy. Time used: 0.108 (sec). Leaf size: 3

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

\[ x{\left (t \right )} = 0 \]