64.20.6 problem 6

Internal problem ID [13649]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 9, The Laplace transform. Section 9.3, Exercises page 452
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 05:54:19 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 9.249 (sec). Leaf size: 22

dsolve([diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=0,y(0) = 2, D(y)(0) = 4],y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[{D[y[t],{t,2}]+2*D[y[t],t]+5*y[t]==0,{y[0]==2,Derivative[1][y][0]==4}},{y[t]},t,IncludeSingularSolutions -> True]
 

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