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Finding the limit and a differential equation

  1. Apr 8, 2007 #1
    i cant seem to figure this out...

    if the differential equation dy/dx= y-2y^2 has a solution curve y=f(x) contianing point (0, 0.25) , then the limit as x approaches infinity of f(x) is



    a)no limit

    b. 0

    c. 0.25

    d. 0.5

    e. 2


    i usually just separate the variables and find f(x) then take the limit, but i cant seem to find f(x) b/c it would require the integral of 1/(y-2y^2)
     
  2. jcsd
  3. Apr 8, 2007 #2
    so, integrate [itex]\frac{1}{y-2y^2}[/itex]! Partial fractions will do it.
     
  4. Apr 8, 2007 #3
    yeah i know...
    i get the equation

    y= 1/(e^-x + 2) +C
    without the c value it is 1/2 for the limit
    but with the c value which is -1/12 i get a limit of 5/12 which is not an answer choice...

    so the question becomes, does the limit depend on the c value or not?
     
  5. Apr 8, 2007 #4
    That's not the answer I get for y(x). Try checking your work again. If you still can't figure it out, post what you've done and I'll try to tell you what's wrong!
     
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