74.10.27 problem 27

Internal problem ID [16232]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 27
Date solved : Tuesday, January 28, 2025 at 08:58:04 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 20

dsolve([diff(y(t),t$2)+4*diff(y(t),t)+20*y(t)=0,y(0) = 2, D(y)(0) = 0],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 22

DSolve[{D[y[t],{t,2}]+4*D[y[t],t]+20*y[t]==0,{y[0]==2,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

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