74.18.33 problem 39

Internal problem ID [16590]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 39
Date solved : Tuesday, January 28, 2025 at 09:11:53 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+10 y^{\prime }+16 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 17

dsolve([diff(y(t),t$2)+10*diff(y(t),t)+16*y(t)=0,y(0) = 0, D(y)(0) = 4],y(t), singsol=all)
 

\[ y = \frac {2 \,{\mathrm e}^{-2 t}}{3}-\frac {2 \,{\mathrm e}^{-8 t}}{3} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 21

DSolve[{D[y[t],{t,2}]+10*D[y[t],t]+16*y[t]==0,{y[0]==0,Derivative[1][y][0] ==4}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {2}{3} e^{-8 t} \left (e^{6 t}-1\right ) \]