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Bernoulli Differential Equations

  1. Oct 8, 2006 #1
    Solve the equation [tex] \frac{dy}{dx}-y = -xe^{-2x}y^{3} [/tex].

    So a Bernoulli differential equation is in the form [tex] \frac{dy}{dx} + P(x)y = Q(x)y^{n} [/tex]. Isn't the above equation in this form already?

    I set [tex] u = y^{-2} [/tex] and [tex] \frac{du}{dx} = -2y^{-3 [/tex].

    So [tex] -2y^{-3} + 2y^{-2} = 2xe^{-2x} [/tex]. From here what do I do?

    Is the integrating factor [tex] I(x) = e^{\int -1 dx} = e^{-x} [/tex]?

  2. jcsd
  3. Oct 8, 2006 #2
    nvm got it.
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