65.6.14 problem 12.1 (xiv)

Internal problem ID [13763]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number : 12.1 (xiv)
Date solved : Tuesday, January 28, 2025 at 06:02:18 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=27\\ y^{\prime }\left (0\right )&=-54 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 10

dsolve([diff(y(t),t$2)+4*diff(y(t),t)+4*y(t)=0,y(0) = 27, D(y)(0) = -54],y(t), singsol=all)
 

\[ y = 27 \,{\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 12

DSolve[{D[y[t],{t,2}]+4*D[y[t],t]+4*y[t]==0,{y[0]==27,Derivative[1][y][0] ==-54}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 27 e^{-2 t} \]