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Solution 1. order differential equation

  1. Jan 9, 2012 #1
    1. The problem statement, all variables and given/known data
    So I've been given an assignment to find all solutions to the differential equation as mentioned below. From what can be seen, it's a 1. order differerential equation.

    The assignment is as stated:

    [itex]

    y'(t)+p*y(t)=y(t)^2

    [/itex]

    2. Relevant equations

    So I tried to rewrite to somehow match the general form of a 1. order differential equation:

    [itex]y'(x) +p(x)y = q(x)[/itex]

    But no matter what I try, I can't get it to look somehow like it.

    3. The attempt at a solution

    The problem is that it equals the funktion itself raised in 2. I just have no idea how to find the solution, when that is the case. I tried to rewrite and solve it, using the general solution, but no matter what, the function itself becomes a part of the solution, which shouldn't be the case.

    Been using the general solution as mentioned below:

    [itex]e^{-µ(x)} * ∫e^{µ(x)} q(x)dx[/itex]

    where [itex] µ(x) = ∫p(x)dx [/itex]

    and [itex] µ(x) = px [/itex]
     
  2. jcsd
  3. Jan 9, 2012 #2

    fluidistic

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    Gold Member

  4. Jan 10, 2012 #3
    "e^{-µ(x)} * ∫e^{µ(x)} q(x)dx,µ(x) = ∫p(x)dx,µ(x) = px" You said µ(x)=px, but p is a function of x, so I believe it's something else. Also I think you meant not the first order since the original diff. equ is already of first order but of first degree.
     
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