14.8.3 problem 3

Internal problem ID [2558]
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 : 3
Date solved : Monday, January 27, 2025 at 06:00:24 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(t),t$2)+2*diff(y(t),t)+3*y(t)=0,y(t), singsol=all)
 

\[ y = {\mathrm e}^{-t} \left (c_1 \sin \left (\sqrt {2}\, t \right )+c_2 \cos \left (\sqrt {2}\, t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 34

DSolve[D[y[t],{t,2}]+2*D[y[t],t]+3*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \left (c_2 \cos \left (\sqrt {2} t\right )+c_1 \sin \left (\sqrt {2} t\right )\right ) \]