Question

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Answer 1

Step-by-step explanation:

this is proved that left hand side = right hand side

Answer 2

Step-by-step explanation:

y' = 6+ e^3x.b + 3.e^3x.(a+bx)  

y" = e^3x.3b + 9.e^3x.(a+bx) + 3.e^3x.b

     = 3be^3x + 9e^3x.(a+bx) + 3be^3x

y" - 6y'  = 3be^3x + 9e^3x.(a+bx) +3be^3x -36 - 6be^3x- 18e^3x.(a+bx)

            = 9e^3x.(a+bx) - 18e^3x.(a+bx) - 36

             = - 9e^3x.(a+bx) - 36

y" - 6y +9y  = -9e^3x.(a+bx) - 36 + 54(x+1) +9(a+bx) e^3x

                   = -36 + 54(x+1)

                   = 54x + 18

°_° (proved)

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