63.15.6 problem 6(f)

Internal problem ID [13189]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 3, Laplace transform. Section 3.2.1 Initial value problems. Exercises page 156
Problem number : 6(f)
Date solved : Tuesday, January 28, 2025 at 05:12:08 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 )&=0 \end{align*}

✓ Solution by Maple

Time used: 6.973 (sec). Leaf size: 5

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

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 6

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

\[ x(t)\to 1 \]