1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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/dx=-5xy

    dy/y=-5x dx

    ∫(1/y)dy=∫-5x dx

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

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


    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

    LCKurtz

    User Avatar
    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
    Yep.

    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted