75.33.11 problem 840

Internal problem ID [17293]
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 : Tuesday, January 28, 2025 at 09:58:58 AM
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*}

✓ Solution by Maple

Time used: 8.462 (sec). Leaf size: 9

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 10

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

\[ x(t)\to -t-1 \]