67.3.3 problem Problem 4

Internal problem ID [14021]
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 4
Date solved : Tuesday, January 28, 2025 at 06:12:55 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 8.820 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 14

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

\[ y(t)\to e^{-t} (t-1) \]