74.10.29 problem 29

Internal problem ID [16234]
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 : 29
Date solved : Tuesday, January 28, 2025 at 08:58:09 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }+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: 0.035 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 47

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

\[ y(t)\to \frac {1}{3} e^{-t/2} \left (\sqrt {3} \sin \left (\frac {\sqrt {3} t}{2}\right )+3 \cos \left (\frac {\sqrt {3} t}{2}\right )\right ) \]