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Thread: numerical solutions/uniqueness of a D.E

  1. #1
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    numerical solutions/uniqueness of a D.E

    ok

    I have two equations;
    (1) d^2y/dx^2 + x^2.y^2 = x, y(0) = y(2) = 0
    (2) d^2y/dx^2 + x^2.y^2 = x, y(0) = 0, y'(0) = -0.7

    I cant solve these algebraically since they are non-linear, solving numerically and plotting a solution, I find that these graphs are very similar for x between 0 and 2. (a parabola going through (0,0) and (2,0), with a minimum at about -0.4)

    does this mean that the solution to (1) has the property y'(0)= -0.7?

    so are the differential equations equivalent since a solution can be described uniquely by ivps or boundary conditions/

    many thanks
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  2. #2
    Super Member Rebesques's Avatar
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    Re: numerical solutions/uniqueness of a D.E

    Nope. The solutions to these two problems are not the same.
    The first problem is a boundary value problem, meaning the solution is defined at the two endpoints x=0 and x=2 of the domain of definition.
    The second problem is an initial value problem, where the values for y and y' are fixed at the initial point x=0.

    The first problem is likely to have a periodical solution, the second most surely not.
    Anyway, its a lazy Sunday, I trust theis info is enough.
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