20.21.25 problem Problem 25

Internal problem ID [3952]
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 25
Date solved : Monday, January 27, 2025 at 08:04:55 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=9 \sin \left (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: 2.823 (sec). Leaf size: 19

dsolve([diff(y(t),t$2)+4*y(t)=9*sin(t),y(0) = 1, D(y)(0) = -1],y(t), singsol=all)
 

\[ y = 3 \sin \left (t \right )+\cos \left (2 t \right )-2 \sin \left (2 t \right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 20

DSolve[{D[y[t],{t,2}]+4*y[t]==9*Sin[t],{y[0]==1,Derivative[1][y][0] ==-1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 3 \sin (t)-2 \sin (2 t)+\cos (2 t) \]