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Given a general solution, find the EDO

  1. Dec 6, 2008 #1
    1. The problem statement

    Given the general solution:
    y==(2*c*e^(2x)) / (1+c*e^(2x))
    find the EDO.

    2. The attempt at a solution

    Im tried isolate c*e^(2x), using implicit differentiation:

    y + y*c*e^(2x)==2*c*e^(2x)
    y'+y'*c*e^2x + 2*y*c*e^(2x)==2*2*c*e^(2x)
    y'==c*e^(2x) * (4-y'-2y)
    e^(2x) * c = y'/(4-y'-2*y)

    Replacing in the general solution given in the problem statement i have this EDO:


    But, in mathematica software when i use DSolve over this EDO to find the general solution, it gives a different one.

    What's wrong?

    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Dec 6, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    There is nothing wrong. I suspect that DSolve is just giving a different, equivalent way of writing the solution.
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