69.33.11 problem 840

Internal problem ID [18580]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 3. Section 24.2. Solving the Cauchy problem for linear differential equation with constant coefficients. Exercises page 249
Problem number : 840
Date solved : Thursday, October 02, 2025 at 03:15:05 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-x^{\prime }&=1 \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.083 (sec). Leaf size: 9

ode:=diff(diff(x(t),t),t)-diff(x(t),t) = 1; 
ic:=[x(0) = -1, D(x)(0) = -1]; 
dsolve([ode,op(ic)],x(t),method='laplace');
 

\[ x = -1-t \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 10

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

\begin{align*} x(t)&\to -t-1 \end{align*}

✓ Sympy. Time used: 0.077 (sec). Leaf size: 7

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

\[ x{\left (t \right )} = - t - 1 \]