20.23.11 problem Problem 11

Internal problem ID [3983]
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 10.8. page 710
Problem number : Problem 11
Date solved : Monday, January 27, 2025 at 08:05:42 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 5.875 (sec). Leaf size: 29

dsolve([diff(y(t),t$2)+9*y(t)=15*sin(2*t)+Dirac(t-Pi/6),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = -\frac {\cos \left (3 t \right ) \operatorname {Heaviside}\left (t -\frac {\pi }{6}\right )}{3}-2 \sin \left (3 t \right )+3 \sin \left (2 t \right ) \]

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 34

DSolve[{D[y[t],{t,2}]+9*y[t]==15*Sin[2*t]+DiracDelta[t-Pi/6],{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {1}{3} \theta (6 t-\pi ) \cos (3 t)+3 \sin (2 t)-2 \sin (3 t) \]