Question

1.Solve : (D2 - 6DD' + 9D*2) z = 6x + 2y.find P.I.​

Answer 1

1.Solve : (D2 - 6DD' + 9D*2) z = 6x + 2y.find P.I.

Answer 2

P.I of the equation ,

D^2 - 6DD' + 9D^2) z = 6x + 2y is [(x^2)/4](3x+y)

◆Considering LHS,

(D^2 - 6DD' + 9D^2) z = 0

m^2 - 6m + 9 = 0

(m - 3)^2 = 0

m =3,3

◆P.I is

[1 /(D^2 - 6DD' + 9D^2) z] (6x + 2y ) = 1 / [(D- 3D')^2](6x + 2y )

◆F(D,D') = (D- 3D' )^2

◆Here,

a=6,b =2

◆F(a,b) =( a- 3b)^2

Substituting values,

(6-3×2)^2 =0

◆P.I = 1 / [(D- 3D')^2](6x + 2y )

= (x^2)/2[(6x+2y)/2^2]

= (x^2)/4(3x+y)

Hence the solution.