7.18.4 problem 4

Internal problem ID [533]
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 : 4
Date solved : Monday, January 27, 2025 at 02:54:39 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+8 x^{\prime }+15 x&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=-3 \end{align*}

✓ Solution by Maple

Time used: 0.200 (sec). Leaf size: 18

dsolve([diff(x(t),t$2)+8*diff(x(t),t)+15*x(t)=0,x(0) = 2, D(x)(0) = -3],x(t), singsol=all)
 

\[ x \left (t \right ) = {\mathrm e}^{-4 t} \left (2 \cosh \left (t \right )+5 \sinh \left (t \right )\right ) \]

✓ Solution by Mathematica

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

DSolve[{D[x[t],{t,2}]+8*D[x[t],t]+15*x[t]==0,{x[0]==2,Derivative[1][x][0] ==-3}},x[t],t,IncludeSingularSolutions -> True]
 

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