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Find the particular integral of the following differential equations.(Explain each step clearly) (a) d2y/dx2 + y =...

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Advance Math

Find the particular integral of the following differentialequations.(Explain each step clearly)

(a) d2y/dx2 + y = (x + 1) sin x. show thatthe answer is yp(x) = ? 1/8 [ (2x2 + 4x ? 1) cos x ? (2x+ 2) sin x ]

(Hint:In this case, we substitute sin ?x or cos ?x withei?x then use the shift operator. In the case of sin ?xwe extract the imaginary part.)

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