74.10.6 problem 6

Internal problem ID [16211]
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 : 6
Date solved : Tuesday, January 28, 2025 at 08:57:17 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

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

\[ y = c_{1} {\mathrm e}^{\frac {\left (-5+\sqrt {21}\right ) t}{2}}+c_{2} {\mathrm e}^{-\frac {\left (5+\sqrt {21}\right ) t}{2}} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 35

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

\[ y(t)\to e^{-\frac {1}{2} \left (5+\sqrt {21}\right ) t} \left (c_2 e^{\sqrt {21} t}+c_1\right ) \]