28.3.7 problem 6.42

Internal problem ID [4520]
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 : 6.42
Date solved : Monday, January 27, 2025 at 09:22:39 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t} \sin \left (2 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: 3.725 (sec). Leaf size: 16

dsolve([diff(y(t),t$2)-2*diff(y(t),t)+5*y(t)=8*exp(t)*sin(2*t),y(0) = 1, D(y)(0) = -1],y(t), singsol=all)
 

\[ y = \left (-2 t +1\right ) {\mathrm e}^{t} \cos \left (2 t \right ) \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 19

DSolve[{D[y[t],{t,2}]-2*D[y[t],t]+5*y[t]==8*Exp[t]*Sin[2*t],{y[0]==1,Derivative[1][y][0] == -1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -e^t (2 t-1) \cos (2 t) \]