57.9.14 problem 2(b)

Internal problem ID [14422]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.3.1 Nonhomogeneous Equations: Undetermined Coefficients. Exercises page 110
Problem number : 2(b)
Date solved : Thursday, October 02, 2025 at 09:37:00 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{\prime \prime }-x^{\prime }&=6+{\mathrm e}^{2 t} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(diff(x(t),t),t)-diff(x(t),t) = 6+exp(2*t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = \frac {{\mathrm e}^{2 t}}{2}+{\mathrm e}^{t} c_1 -6 t +c_2 \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 26

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

\begin{align*} x(t)&\to -6 t+\frac {e^{2 t}}{2}+c_1 e^t+c_2 \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 19

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

\[ x{\left (t \right )} = C_{1} + C_{2} e^{t} - 6 t + \frac {e^{2 t}}{2} \]