74.10.26 problem 26

Internal problem ID [16231]
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 : 26
Date solved : Tuesday, January 28, 2025 at 08:58:01 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 21

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

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

✓ 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]==1,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

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