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Separable Differential Equation Question

  1. Jan 5, 2013 #1
    1. The problem statement, all variables and given/known data
    dy/dx = (y^2 - 1)/ (x^2 - 1) with initial condition y(2) = 2

    Why is y = 1 and/or y= -1 not solutions?

    2. Relevant equations

    3. The attempt at a solution

    I am actually able to solve this differential equation but when I separate the equation according to x and y:

    (y^2 - 1)^-1 dy = (x^2 - 1)^-1 dx

    here I am dividing both sides of the equation by (y^2 - 1), which means now I have to exclude y = 1 , -1 and check whether they are solutions

    Now how do I show that y =1 and y = -1 are not solutions?
  2. jcsd
  3. Jan 5, 2013 #2


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    Science Advisor
    Homework Helper

    y=1 or y=(-1) don't satisfy y(2)=2, do they? They are solutions to the differential equation but they don't satisfy your boundary condition.
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