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Homework Help: One more 2nd order D.E.

  1. Nov 13, 2005 #1
    for the following question:
    y``+y`+9.25y=2+2x+x^2

    my problem:
    yh=c1+c2e^(-x)
    suppose yp=c3x^2 + c4x+c5
    then yp`=2c3x+c4
    so yp``=2c3

    then 2c3+2c3x+c4=2+2X+X^2
    so c3=1, c4=1
    so yp=x^2+x
    then y=c1+c2e^(-x)+x^2+x
    which implies c1=8
    => y=8+c2e^(-x)+x^2+x
    so y`=-c2e^(-x)+2x+1
    so -1=-c2+1 =>c2=2
    then y=8+2e^(-x)+x^2 +x

    but the correct answer should be 3e^(-x)+5+2x+(1/3)x^3
    does anybody know what's wrong with the calculations?
     
  2. jcsd
  3. Nov 13, 2005 #2
    According to what you have written your homogeneous solution isn't a homogeneous solution:

    (c_2e^(-x))+(-c_2e^(-x))+9.25(c_1+c_2e^(-x))=9.25(c_1+c_2e^(-x)) which isn't zero (unless both constants are zero)
     
  4. Nov 13, 2005 #3
    jeepers!!! i'll recheck that again! thanks!!!
     
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