14.8.1 problem 1

Internal problem ID [2556]
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 : 1
Date solved : Monday, January 27, 2025 at 06:00:19 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 28

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

\[ y = {\mathrm e}^{-\frac {t}{2}} \left (c_1 \sin \left (\frac {\sqrt {3}\, t}{2}\right )+c_2 \cos \left (\frac {\sqrt {3}\, t}{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 42

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

\[ y(t)\to e^{-t/2} \left (c_2 \cos \left (\frac {\sqrt {3} t}{2}\right )+c_1 \sin \left (\frac {\sqrt {3} t}{2}\right )\right ) \]