11.3.5 problem 12

Internal problem ID [1487]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 6.2, The Laplace Transform. Solution of Initial Value Problems. page 255
Problem number : 12
Date solved : Monday, January 27, 2025 at 04:57:52 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 )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.267 (sec). Leaf size: 21

dsolve([diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=0,y(0) = 2, D(y)(0) = -1],y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-t} \left (4 \cos \left (2 t \right )+\sin \left (2 t \right )\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 25

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

\[ y(t)\to \frac {1}{2} e^{-t} (\sin (2 t)+4 \cos (2 t)) \]