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How do I solve this seperable equation?

  1. Feb 5, 2017 #1
    1. The problem statement, all variables and given/known data
    This is just something I am doing for fun. If you see my attachment you will see I took an equation (underlined) and differentiated it implicitly to give me a separable equation (boxed)

    How do I solve the separable equation to work backwards to get the underlined equation?

    I apologize in advance, I forgot to bring the negative sign into the separable equation.

    2. Relevant equations
    in attachment

    3. The attempt at a solution
    in attachment
     

    Attached Files:

  2. jcsd
  3. Feb 5, 2017 #2

    Mark44

    Staff: Mentor

    From your attachment, here's what you have:
    ##y^2 + 2xy = C##
    ##2y\frac{dy}{dx} + 2y + 2x\frac{dy}{dx} = 0##
    ##\frac{dy}{dx} 2x + 2y = -2y##
    ##\frac{dy}{dx} = \frac{-y}{x + y}## (added the minus sign that you mentioned)

    The third line needs parentheses around 2x + 2y.
    Your final equation is not separable. Another tactic must be used. One that works is to let u = y/x. That will give you a separable DE.
     
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