20.21.22 problem Problem 22

Internal problem ID [3949]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.4. page 689
Problem number : Problem 22
Date solved : Monday, January 27, 2025 at 08:04:53 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=20 \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 )&=2 \end{align*}

✓ Solution by Maple

Time used: 2.605 (sec). Leaf size: 23

dsolve([diff(y(t),t$2)+5*diff(y(t),t)+4*y(t)=20*sin(2*t),y(0) = -1, D(y)(0) = 2],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 27

DSolve[{D[y[t],{t,2}]+5*D[y[t],t]+4*y[t]==20*Sin[2*t],{y[0]==-1,Derivative[1][y][0] ==2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t} \left (2 e^{3 t}-1\right )-2 \cos (2 t) \]