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!

Homework Help: DE homework problem

  1. Feb 14, 2006 #1
    Consider dy/dt = 2*(abs(sqrt(y)))

    1.Show that y(t)=0 is a solution for all t.
    I did this part

    2.Find all solutions (hint, give solution like y(t)=... for t>=0, y(t)=... t<0).
    He told us in class that t=0 isn't necessarily the point we should be concerned with

    3.Why doesn't this contradict the uniqueness theorem?
    I have a feeling it's because our DE isn't differentiable at y=0, but my main problem is number 2.

    I graphed this DE on the computer, so assuming I typed it in right I know what it looks like. I also tried splitting the DE up into cases for part 2, but it seems that I would have to perform the same integral twice which doesn't really make sense.
  2. jcsd
  3. Feb 14, 2006 #2


    User Avatar
    Homework Helper

    Could you show your work then? There should be a small difference...
    Remember the definition of the absolute value.
  4. Feb 14, 2006 #3
    dy/dt = 2*sqrt(abs(y)) = 2*sqrt(y) y>=0, 2*sqrt(-y) y<0

    isn't 2*sqrt(-y) when y<0 = 2*sqrt(y)
  5. Feb 14, 2006 #4
    I have y(t) = (t-C)^2 when y>=0. I get the same thing when y<0 as well, by seperation of variables. I use t-C rather than t+C thanks to a hint from my professor from yesterday's lecture. So, is this the solution I am looking for?
  6. Feb 15, 2006 #5


    User Avatar
    Homework Helper

    The initial problem was "abs(sqrt(y))" and now you write "sqrt(abs(y))", which one is it?
  7. Feb 15, 2006 #6


    User Avatar
    Science Advisor

    "isn't 2*sqrt(-y) when y<0 = 2*sqrt(y)"

    No, it's not. For example if y= -4, 2*sqrt(-y)= 2*sqrt(4)= 4 but
    2*sqrt(y)= 2*sqrt(-4)= 4i.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook