75.33.10 problem 839

Internal problem ID [17213]
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 : 839
Date solved : Thursday, March 13, 2025 at 09:18:55 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+x^{\prime }&=0 \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: 7.690 (sec). Leaf size: 8

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

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 10

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

\[ x(t)\to e^{-t} \]

✓ Sympy. Time used: 0.115 (sec). Leaf size: 7

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

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