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Math Help - Boundary or initial?

  1. #1
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    Boundary or initial?

    1) I have been asked to classify some differential equations as boundary or initial problems. With a first order ordinary DE does this even make sense? There is only one condition to be met y(a) = b

    2) If the dependent variable is subject to a modulus operation in one of its terms, does this make the differential equation non-linear?
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  2. #2
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    Quote Originally Posted by mdruett View Post
    1) I have been asked to classify some differential equations as boundary or initial problems. With a first order ordinary DE does this even make sense? There is only one condition to be met y(a) = b

    2) If the dependent variable is subject to a modulus operation in one of its terms, does this make the differential equation non-linear?
    1) y(a) = b is an initial condition if a = 0. Otherwise it's called a boundary condition.

    2) |y| = y if y > 0 and |y| = -y if y < 0 ....
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    thanks, but further clarification req.

    1) This is not a time equation necessarily. In second order equations we still have an initial condition problem if y(a) = b and y'(a) = c as I understand it... Does your position remain the same?

    2) I understand what the modulus function implies about the value of y. My question is "does this classify as non-linear behavior?" I Suspect yes. It's the definition of a linear equation that I require clarification of, rather than the modulus function.
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  4. #4
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    Quote Originally Posted by mdruett View Post
    1) This is not a time equation necessarily. In second order equations we still have an initial condition problem if y(a) = b and y'(a) = c as I understand it... Does your position remain the same?
    Like Mr F said, it is called an "initial condition" when the value you are given of your independent variable is 0. This is simply because intuitively this is where we interpret the independent variable as starting. So it doesn't matter if the independent variable is time or not.
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    Thanks

    If I knew how to thank, you would both be thanked!
    It'll have to be verbal until then!
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