63.15.3 problem 6(c)

Internal problem ID [13186]
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(c)
Date solved : Tuesday, January 28, 2025 at 05:12:06 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-x^{\prime }-6 x&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 8.438 (sec). Leaf size: 18

dsolve([diff(x(t),t$2)-diff(x(t),t)-6*x(t)=0,x(0) = 2, D(x)(0) = -1],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\left (3 \,{\mathrm e}^{5 t}+7\right ) {\mathrm e}^{-2 t}}{5} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 23

DSolve[{D[x[t],{t,2}]-D[x[t],t]-6*x[t]==0,{x[0]==2,Derivative[1][x][0 ]==-1}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{5} e^{-2 t} \left (3 e^{5 t}+7\right ) \]