74.18.32 problem 38

Internal problem ID [16589]
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 : 38
Date solved : Tuesday, January 28, 2025 at 09:11:51 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 17

dsolve([diff(y(t),t$2)+5*diff(y(t),t)+6*y(t)=0,y(0) = 2, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = -4 \,{\mathrm e}^{-3 t}+6 \,{\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 18

DSolve[{D[y[t],{t,2}]+5*D[y[t],t]+6*y[t]==0,{y[0]==2,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} \left (6 e^t-4\right ) \]