76.18.3 problem 14

Internal problem ID [17714]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 5. The Laplace transform. Section 5.2 (Properties of the Laplace transform). Problems at page 309
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 11:01:44 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 )&=3\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 10.863 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

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

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

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