Question

[(x + 2)² D^2- (x+2)D + 1 ] y = 3x +4

Answer 1

Step-by-step explanation:

(D^2 +2D+1) y= 2e^3x

A.E= m^2+2m+1 = 0

=> (m+1) (m+1) = 0

=> m = - 1 , - 1

Hence roots of AE is real and equal, therefore

C. F= (c1 +c2 x) e^ -x

P.I = 2e^3x/(D^2 +2D +1)

P. I= 2e^3x/[(3) ^2+2(3) +1]

P. I= 2e^3x/16

P. I = e^3x/8

Hence, y = C. F + P. I

=> y = (c1 + c2 x) e^-x + e^3x/8