1.

Find the solution of the differential equation 4y”’ + 4y” + y’ = 0.

Answer»

The given equation in symbolic form is written as (4D3 + 4D2 + D)y = 0 and its auxiliary equation is 

4D3 + 4D2 + D = 0

D(4D2 + 4D + 1) = 0 D(2D + 1)2 = 0

i.e D = 0, - 1/2, - 1/2

whence (C.F) = c1e0 + (c2x + c3)e-x/2.



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