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Homework Help: Help! I don't understand about equailities of the eqation.

  1. Mar 7, 2014 #1
    1. The problem statement, all variables and given/known data

    y'=-5xy, y=?

    3. The attempt at a solution

    i solved that,


    dy/y=-5x dx

    ∫(1/y)dy=∫-5x dx

    = ln(lyl)= -2.5x^2+C

    so, y=+- e^(-2.5x^2+C)

    but the answer is y=K*e^(-2.5x^2)

    how can i understand this?

    just shoud i ignore "the absolute value"?
  2. jcsd
  3. Mar 7, 2014 #2


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    Science Advisor
    Homework Helper
    Gold Member

    In your solution ##K = \pm e^C## which can be anything but zero. In the answer ##K## is unrestricted. So the only difference is that the answer includes ##y=0## and your solution doesn't. (It was missed when you divided by ##y##). The answers are the same once you include ##y=0## in yours.
  4. Mar 7, 2014 #3

    The only reason |abs| is used is to mark the fact that it's impossible to have a ln() value where the thing in the brackets is negative.

    Essentially y must be positive for the equation to work.

    The only time I can think of that you really need to use +/- is when you have a value with an even power, such as x2, x4, x-6, etc. Because then x can be positive or negative and will still yield the same result when you raise it to that power.

    Hope that helps a little!
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