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Solve d^3y/dx^3 + d^2y/dx^2 + 4dy/dx + 4y = x^2 - 4x - 6.

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Solve d3y/dx3 + d2y/dx2 + 4dy/dx + 4y = x2 - 4x - 6.

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1 Answer

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Best answer

We have 

(D3 + D2 + 4D + 4)y = x2 – 4x – 6 

A.E. is m3 + m2 + 4m + 4 = 0 

m2(m + 1) + 4(m + 1) = 0

(m + 1) (m2 + 4) = 0 

m = – 1, m = ± 2i

∴ C.F. = C1 e–x + C2cos2x + C3sin2x

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