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solve (D^2+2D+1)y=2x+x^2 please tell me the answer fastly urgent please

solve (D^2+2D+1)y=2x+x^2 please tell me the answer fastly urgent please
 
 

Grade:12th pass

1 Answers

Nandana
110 Points
3 years ago
hi ,
 y(x) =yc (x) + yp (x)
 finding  yc (x) :
    D^2+2D+1 = 0
     D = -1
      yc (x) = A e-x + Bx e-x
finding yp (x) :
    by substituting
    Y (x) = a x2 +bx +c
   d2/dx2 (a x2 +bx +c) + 2 d/dx ( a x2 +bx +c) + a x2 +bx +c = x2 + 2x
           2a + 4ax +2b + a x2 +bx +c  =  x2 + 2x
              a = 1
              2a +c+2b = 0
             4a +b = 2
                  b =-2
                 c = 2
          yp (x)  = x2 -2x +2
over all solution
     y(x) = A e-x + Bx e-x + x2 -2x +2
      A,B are orbitary constants

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