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Bernoulli - Find the general solution

  1. Sep 22, 2011 #1
    Bernoulli -- Find the general solution

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

    Find the general solution of:

    y'+xy=xy^3


    2. Relevant equations

    Bernoulli's Equation


    3. The attempt at a solution

    y'+xy=xy^3

    (y^-3)y'+x(y^-2)=x

    Let v=(y^-2), thus v'=((-2y^-3)y'

    Then,

    -v'/2+xv=x

    Multiply through by (-2)

    v'-2xv=-2x

    Now it's in first-order linear so I multiply by e^int(-2x)dx = e^(-x^2)

    (e^(-x^2))v'-2xe^(-x^2)=2xe^(-x^2)

    This is where I'm getting stuck :(

    BECAUSE: the integral of e^(-x^2) is the "error function?"

    According to Wolfram, integral e^(-x^2) dx = 1/2 sqrt(pi) erf(x)+constant

    ----

    Anyone get anything different or know where I might have messed up?

    THANK YOU!!
     
  2. jcsd
  3. Sep 22, 2011 #2
    Re: Bernoulli -- Find the general solution

    GOT IT!! Sorry, I don't know if there's an option for deleting a topic. My apologies.

    Thanks, either way :)
     
  4. Sep 22, 2011 #3

    rude man

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    Homework Helper
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    Re: Bernoulli -- Find the general solution

    Should have used separation of variables.
     
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