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Bernoulli differential equation

  1. Jan 22, 2009 #1
    1. The problem statement, all variables and given/known data

    Solve the Bernoulli equation,

    y'(x) - 4y(x) = 2e^(x) * sqrt(y(x))

    2. Relevant equations

    y' + P(x)y = Q(x)y^n - Bernoulli Eqn
    e^(∫P(x) dx) - Integrating Factor

    3. The attempt at a solution

    y' - 4y = 2e^(x) * y^(1/2)

    Divided both sides by y^(1/2)

    y'/y^(1/2) - 4y/y^(1/2) = 2e^(x)

    y'/y^(1/2) - 4y^(1/2) = 2e^(x)

    My problem comes when changing variables. What am I supposed to choose for 'u' (the variable I'll be changing to)? Just y^(1/2)? My text and notes aren't very clear on this.
     
    Last edited: Jan 22, 2009
  2. jcsd
  3. Jan 22, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    Yes put u=y1/2

    In general, for:

    [tex]\frac{dy}{dx}+P(x)y=Q(x)y^n[/tex]

    put [itex]u=y^{1-n}[/itex]
     
  4. Jan 22, 2009 #3
    Alright, thank you for your help.
     
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