65.7.11 problem 14.1 (xi)

Internal problem ID [13696]
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 : Wednesday, March 05, 2025 at 10:13:03 PM
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: 0.005 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 50

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]
 

\[ x(t)\to \frac {1}{4} e^{-2 t} \left (4 \int _1^t-e^{4 K[1]} K[1]dK[1]+e^{4 t} t+4 (c_2 t+c_1)\right ) \]

✓ Sympy. Time used: 0.190 (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)
 

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