80.5.17 problem B 17

Internal problem ID [21238]
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 17
Date solved : Thursday, October 02, 2025 at 07:27:11 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 38

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

\[ x = \left (c_1 \,{\mathrm e}^{2 t \sqrt {a^{2}-b}}+c_2 \right ) {\mathrm e}^{\left (a -\sqrt {a^{2}-b}\right ) t} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 48

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

\begin{align*} x(t)&\to c_1 e^{t \left (a-\sqrt {a^2-b}\right )}+c_2 e^{t \left (\sqrt {a^2-b}+a\right )} \end{align*}

✓ Sympy. Time used: 0.121 (sec). Leaf size: 32

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

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