80.5.43 problem C 19

Internal problem ID [21264]
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 : C 19
Date solved : Thursday, October 02, 2025 at 07:27:28 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }-4 x^{\prime }+3 x&=2 \,{\mathrm e}^{t}-5 \,{\mathrm e}^{2 t} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=diff(diff(x(t),t),t)-4*diff(x(t),t)+3*x(t) = 2*exp(t)-5*exp(2*t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = -{\mathrm e}^{t} \left (-c_2 -c_1 \,{\mathrm e}^{2 t}+t -5 \,{\mathrm e}^{t}+\frac {1}{2}\right ) \]

✓ Mathematica. Time used: 0.089 (sec). Leaf size: 35

ode=D[x[t],{t,2}]-4*D[x[t],t]+3*x[t]==2*Exp[t]-5*Exp[2*t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {1}{2} e^t \left (-2 t+10 e^t+2 c_2 e^{2 t}-1+2 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.125 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(3*x(t) + 5*exp(2*t) - 2*exp(t) - 4*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \left (C_{1} + C_{2} e^{2 t} - t + 5 e^{t}\right ) e^{t} \]