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Second order differential equation

  1. May 26, 2013 #1
    Find a solution to the following second order differential equation
    xy'+y=1/y^2

    My Attempt:

    P= y'= dy/dx

    x dy/dx + y = 1/y^2

    dy/dx + y/x = 1/xy^2

    Integrating Factor = e^∫1/x dx = e^lnx

    y e^lnx=∫ (e^lnx)(1/xy^2) dx
     
  2. jcsd
  3. May 26, 2013 #2
    I do not see how this equation is second-order. Where is the second derivative of y?

    So where are you stuck? What are you doing?

    It bothers me a little that you seem to be using an integrating factor on a nonlinear differential equation; typically, multiplying by an integrating factor is something you do when the the DE is linear (this one isn't since you have a y^2 term).

    This differential equation is nonlinear, so it must be one of the types that can be solved explicitly (if this is a homework problem). Can it be shown to be exact, homogeneous, or Bernoulli? (Hint: it can.)
     
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