7.18.3 problem 3

Internal problem ID [532]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 4. Laplace transform methods. Section 4.2 (Transformation of initial value problems). Problems at page 287
Problem number : 3
Date solved : Monday, January 27, 2025 at 02:54:39 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-x^{\prime }-2 x&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.194 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 21

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

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