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Calculus: Solve the following differential equation

  1. Jun 9, 2005 #1
    Solve the following differential equation:

    8y'' - 4x = 0 Where y= 2 and y'=-3 and x= 0

    first i did this:

    y' = (1/4)x^2

    y' = (1/4)x^2 - 3

    then antideriv again to get the final answer:

    y = (x^3)/12 - 3x + 2

    is the final answer 2 or this one :y = (x^3)/12 - 3x + 2

    THANK YOU!
     
  2. jcsd
  3. Jun 9, 2005 #2

    OlderDan

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    I think they are looking for the function y = f(x) rather than the specific value y = f(0). You would not need to solve the equation to find the latter, because it is given. The wording of the intitial conditions would be better stated as

    Where y= 2 and y'=-3 at (or when) x= 0
     
  4. Jun 9, 2005 #3
    so did i get it wrong this is all it said for the question:

    Solve the following differential equation:

    8y'' - 4x = 0 Where y= 2 and y'=-3 at x= 0
     
  5. Jun 9, 2005 #4

    OlderDan

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    You did it correctly. I thought you were just trying to decide between the function you found and the specific value y = 2.

    y = (x^3)/12 - 3x + 2 looks good to me.
     
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