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

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

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

(Hint:In this case, we substitute sin αx or cos αx with e^iαx then use the shift operator. In the case of sin αx we extract the imaginary part.)

Expert Solution

Colby Messinger answered 2 years ago

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