74.10.14 problem 14

Internal problem ID [16219]
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 : 14
Date solved : Tuesday, January 28, 2025 at 08:57:34 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 20

DSolve[4*D[y[t],{t,2}]+4*D[y[t],t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t/2} (c_2 t+c_1) \]