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yaro99

  • 3 years ago

Solve the IVP (dirac's delta function)

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  1. yaro99
    • 3 years ago
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    \[y''+y=\delta(t-\pi)-\delta(t-2\pi)\] \[y(0)=0\] \[y'(0)=1\]

  2. yaro99
    • 3 years ago
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    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?

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