65.9.1 problem 16.1 (i)

Internal problem ID [13701]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 16, Higher order linear equations with constant coefficients. Exercises page 153
Problem number : 16.1 (i)
Date solved : Wednesday, March 05, 2025 at 10:13:18 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x&={\mathrm e}^{-t} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 27

ode:=diff(diff(diff(x(t),t),t),t)-6*diff(diff(x(t),t),t)+11*diff(x(t),t)-6*x(t) = exp(-t); 
dsolve(ode,x(t), singsol=all);
 

\[ x \left (t \right ) = -\frac {{\mathrm e}^{-t}}{24}+c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{3 t} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 37

ode=D[x[t],{t,3}]-6*D[x[t],{t,2}]+11*D[x[t],t]-6*x[t]==Exp[-t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to -\frac {e^{-t}}{24}+c_1 e^t+c_2 e^{2 t}+c_3 e^{3 t} \]

✓ Sympy. Time used: 0.220 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-6*x(t) + 11*Derivative(x(t), t) - 6*Derivative(x(t), (t, 2)) + Derivative(x(t), (t, 3)) - exp(-t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} e^{t} + C_{2} e^{2 t} + C_{3} e^{3 t} - \frac {e^{- t}}{24} \]