## anonymous 3 years ago Solve the IVP (dirac's delta function)

1. anonymous

$y''+y=\delta(t-\pi)-\delta(t-2\pi)$ $y(0)=0$ $y'(0)=1$

2. anonymous

I got: $y=\frac{ e^{-\pi*s}-e^{-2*\pi*s}+1 }{ s^2+1 } = \sin(t) u(t-\pi)-\sin(t) u(t-2*\pi)+\sin(t)$ The book's answer is: $\sin(t) (0<t<\pi),$$0 (\pi<t<2\pi)$$-\sin(t) (t>2\pi)$ Is my answer correct, and how would I get it in the above form?