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Math Help - if you have an initial value in a d.e.

  1. #1
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    if you have an initial value in a d.e.

    lets say, y(0)=-2

    what does this mean?

    also what are you then 'solving' for????

    also if you do not have an initial value, what counts as solving it?
    and how do you check an answer against the initial d.e. if you have a constant in the answer? what do you plug into your initial d.e.
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  2. #2
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    It means that when \displaystyle x = 0, y = -2. It's a point that lies on your curve.

    Assuming you have solved a DE, you will have integration constants. You can use known points on the curve to solve the integration constants.
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  3. #3
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    so will the solution be in terms of your constant? given a point x,y (from your initial condition) find the constant?
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  4. #4
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    The initial point allows you to find the constant of integration (usually). The final solution to a first-order IVP should not have an arbitrary constant in it.
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