14.8.6 problem 6

Internal problem ID [2561]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.2.1 Linear equations with constant coefficients (complex roots). Excercises page 144
Problem number : 6
Date solved : Monday, January 27, 2025 at 06:00:33 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 )&=0\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 15

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

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