67.3.11 problem Problem 12

Internal problem ID [14029]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number : Problem 12
Date solved : Tuesday, January 28, 2025 at 06:13:00 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-3 \end{align*}

✓ Solution by Maple

Time used: 9.001 (sec). Leaf size: 8

dsolve([diff(y(t),t$2)+6*diff(y(t),t)+9*y(t)=0,y(0) = 1, D(y)(0) = -3],y(t), singsol=all)
 

\[ y = {\mathrm e}^{-3 t} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 10

DSolve[{D[y[t],{t,2}]+6*D[y[t],t]+9*y[t]==0,{y[0]==1,Derivative[1][y][0] ==-3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} \]