73.19.7 problem 28.8 (d)

Internal problem ID [15605]
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 (d)
Date solved : Tuesday, January 28, 2025 at 08:03:04 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+17 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-12 \end{align*}

✓ Solution by Maple

Time used: 8.731 (sec). Leaf size: 12

dsolve([diff(y(t),t$2)+8*diff(y(t),t)+17*y(t)=0,y(0) = 3, D(y)(0) = -12],y(t), singsol=all)
 

\[ y = 3 \,{\mathrm e}^{-4 t} \cos \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 14

DSolve[{D[y[t],{t,2}]+8*D[y[t],t]+17*y[t]==0,{y[0]==3,Derivative[1][y][0] ==-12}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 3 e^{-4 t} \cos (t) \]