74.10.12 problem 12

Internal problem ID [16217]
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 : 12
Date solved : Tuesday, January 28, 2025 at 08:57:31 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }+21 y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(4*diff(y(t),t$2)+21*diff(y(t),t)+5*y(t)=0,y(t), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-\frac {t}{4}}+c_{2} {\mathrm e}^{-5 t} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 35

DSolve[D[y[t],{t,2}]+21*D[y[t],t]+5*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-\frac {1}{2} \left (21+\sqrt {421}\right ) t} \left (c_2 e^{\sqrt {421} t}+c_1\right ) \]