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Find the PI of (D3+1)y=cos(2x-1) |
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Answer» P.I. = \(\frac{1}{D^3+1}\) cos(2x - 1) = \(\frac{1}{(D+1)(D^2-D+1)}\) cos(2x - 1) = \(\frac{1}{(D+1)(-4-D+1)}\) cos(2x - 1) = \(\frac{1}{(D+1)(-3-D)}\) cos(2x - 1) = \(\frac{-1}{D^2+4D+3}\) cos(2x - 1) = \(\frac{-1}{-4+4D+3}\) cos(2x - 1) = \(\frac{-(4D+1)}{(4D-1)(4D+1)}\) cos(2x - 1) = \(\frac{-(4D+1)}{16D^2-1}\) cos(2x - 1) = \(\frac{-(4D\,cos(2x - 1))+cos(2x-1)}{16\times-4-1}\) = \(\frac{-(-8\,sin(2x-1)+cos(2x-1)}{-65}\) = \(\frac{1}{65}\) cos(2x-1)-8 sin (2x-1) |
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