73.19.6 problem 28.8 (c)

Internal problem ID [15604]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 28. The inverse Laplace transform. Additional Exercises. page 509
Problem number : 28.8 (c)
Date solved : Tuesday, January 28, 2025 at 08:03:03 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 9.261 (sec). Leaf size: 22

dsolve([diff(y(t),t$2)+6*diff(y(t),t)+13*y(t)=0,y(0) = 2, D(y)(0) = 8],y(t), singsol=all)
 

\[ y = {\mathrm e}^{-3 t} \left (2 \cos \left (2 t \right )+7 \sin \left (2 t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 24

DSolve[{D[y[t],{t,2}]+6*D[y[t],t]+13*y[t]==0,{y[0]==2,Derivative[1][y][0] ==8}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} (7 \sin (2 t)+2 \cos (2 t)) \]