67.3.7 problem Problem 8

Internal problem ID [14025]
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 8
Date solved : Tuesday, January 28, 2025 at 06:12:58 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 8.802 (sec). Leaf size: 17

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

\[ y = -5 \,{\mathrm e}^{-2 t}+7 \,{\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 18

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

\[ y(t)\to e^{-2 t} \left (7 e^t-5\right ) \]