Internal problem ID [2385]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y-15 \sin \left (2 t \right )-\left (\delta \left (t -\frac {\pi }{6}\right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \relax (t ) = -2 \sin \left (3 t \right )+3 \sin \left (2 t \right )-\frac {\cos \left (3 t \right ) \theta \left (t -\frac {\pi }{6}\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 34
DSolve[{y''[t]+9*y[t]==15*Sin[2*t]+DiracDelta[t-Pi/6],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {1}{3} \theta (6 t-\pi ) \cos (3 t)+3 \sin (2 t)-2 \sin (3 t) \\ \end{align*}