75.33.10 problem 839

Internal problem ID [17292]
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 : Tuesday, January 28, 2025 at 09:58:58 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*}

✓ Solution by Maple

Time used: 7.690 (sec). Leaf size: 8

dsolve([diff(x(t),t$2)+diff(x(t),t)=0,x(0) = 1, D(x)(0) = -1],x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 10

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

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