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Solving a first order differential equation

  1. Jan 4, 2016 #1
    1. The problem statement, all variables and given/known data

    Solve the differential equation:
    dy/dx = 2/(x+e^y)

    2. Relevant equations

    3. The attempt at a solution

    I tried to use the substitution v=x+e^y, but I didn't get very far:

    v’=1+e^y y’
    y’ = (v’-1)/(v-x)
    (v’-1)/(v-x) (x+v-x)=2
    V (v’-1)/(v-x)=2

    any help will be very much appreciated.
  2. jcsd
  3. Jan 4, 2016 #2


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    Threads for solving differential equations by nature belong in the Calculus HW forum.
  4. Jan 4, 2016 #3


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    Hmm, this last equation is homogeneous, so setting v=ux should allow you to separate variables.
  5. Jan 4, 2016 #4
    use this result to simplify it to a linear differential equation
  6. Jan 4, 2016 #5


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    Oh yes! This works very nicely.

    Use it with the given D.E.
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