20.21.23 problem Problem 23

Internal problem ID [3950]
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 23
Date solved : Monday, January 27, 2025 at 08:04:54 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: 2.321 (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)
 

\[ y = -\frac {{\mathrm e}^{-4 t}}{3}-2 \cos \left (2 t \right )+\frac {10 \,{\mathrm e}^{-t}}{3} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 30

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]
 

\[ y(t)\to \frac {1}{3} e^{-4 t} \left (10 e^{3 t}-1\right )-2 \cos (2 t) \]