59.7.8 problem 14.1 (viii)

Internal problem ID [15053]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 14, Inhomogeneous second order linear equations. Exercises page 140
Problem number : 14.1 (viii)
Date solved : Thursday, October 02, 2025 at 10:02:26 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime }+2 x^{\prime }+10 x&={\mathrm e}^{-t} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(diff(x(t),t),t)+2*diff(x(t),t)+10*x(t) = exp(-t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = {\mathrm e}^{-t} \left (\frac {1}{9}+c_2 \sin \left (3 t \right )+c_1 \cos \left (3 t \right )\right ) \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 32

ode=D[x[t],{t,2}]+2*D[x[t],t]+10*x[t]==Exp[-t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {1}{9} e^{-t} (9 c_2 \cos (3 t)+9 c_1 \sin (3 t)+1) \end{align*}

✓ Sympy. Time used: 0.137 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(10*x(t) + 2*Derivative(x(t), t) + Derivative(x(t), (t, 2)) - exp(-t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \left (C_{1} \sin {\left (3 t \right )} + C_{2} \cos {\left (3 t \right )} + \frac {1}{9}\right ) e^{- t} \]