57.9.22 problem 5

Internal problem ID [14430]
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 : 5
Date solved : Thursday, October 02, 2025 at 09:37:06 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-2 x^{\prime }&=4 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1 \\ x^{\prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 12

ode:=diff(diff(x(t),t),t)-2*diff(x(t),t) = 4; 
ic:=[x(0) = 1, D(x)(0) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = {\mathrm e}^{2 t}-2 t \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 14

ode=D[x[t],{t,2}]-2*D[x[t],t]==4; 
ic={x[0]==1,Derivative[1][x][0 ]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to e^{2 t}-2 t \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-2*Derivative(x(t), t) + Derivative(x(t), (t, 2)) - 4,0) 
ics = {x(0): 1, Subs(Derivative(x(t), t), t, 0): 0} 
dsolve(ode,func=x(t),ics=ics)
 

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