59.7.11 problem 14.1 (xi)

Internal problem ID [15056]
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 (xi)
Date solved : Thursday, October 02, 2025 at 10:02:28 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

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

\[ x = \frac {\left ({\mathrm e}^{4 t}+16 t c_1 +16 c_2 \right ) {\mathrm e}^{-2 t}}{16} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 28

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

\begin{align*} x(t)&\to \frac {e^{2 t}}{16}+e^{-2 t} (c_2 t+c_1) \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 19

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

\[ x{\left (t \right )} = \left (C_{1} + C_{2} t\right ) e^{- 2 t} + \frac {e^{2 t}}{16} \]