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Homework Help: Eliminating constants

  1. Oct 17, 2012 #1
    1. The problem statement, all variables and given/known data

    eliminating c1 and c2 from y, y' and y'' to create a differential equation

    2. Relevant equations

    I have the equation y = (c1 +c2x)e^x
    y' = c2e^x +(c1+c2x)e^x
    y'' = c2e^x + c2e^x + (c1+c2x)e^x)

    (from product rule)

    3. The attempt at a solution

    I'm just not sure how to eliminate the constants. If I try to do y'' - y i still have constants left.
  2. jcsd
  3. Oct 17, 2012 #2


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    What do you get if you plug y = (c1 +c2x)ex for the second term in y' ?

    Solve that for c2.
  4. Oct 17, 2012 #3
    with y"-y you are only using part of you available information.
    What happens if you subtract y-y' = ... ?
    or y'-y" ?
  5. Oct 17, 2012 #4
    thank you! I can't believe I didn't see that.

    I got c2 = (y' - y)/ e^x. I can then sub this into y'' to get the differential.

    Thank you :)
    Last edited: Oct 17, 2012
  6. Oct 17, 2012 #5
    Isn't it c2 = (y' - y) e^-x ?
  7. Oct 17, 2012 #6
    yes yes, for some reason it didn't put the / button
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