28.3.1 problem 6.36

Internal problem ID [4514]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 6. The Laplace Transform and Its Applications. Problems at page 291
Problem number : 6.36
Date solved : Monday, January 27, 2025 at 09:22:35 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=60 \cos \left (3 t \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 3.215 (sec). Leaf size: 29

dsolve([diff(y(t),t$2)+4*diff(y(t),t)+3*y(t)=60*cos(3*t),y(0) = 1, D(y)(0) = -1],y(t), singsol=all)
 

\[ y = 5 \,{\mathrm e}^{-3 t}-2 \cos \left (3 t \right )+4 \sin \left (3 t \right )-2 \,{\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 33

DSolve[{D[y[t],{t,2}]+4*D[y[t],t]+3*y[t]==60*Cos[3*t],{y[0]==1,Derivative[1][y][0] == -1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} \left (5-2 e^{2 t}\right )+4 \sin (3 t)-2 \cos (3 t) \]