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Math Help - ODE-Determining whether differential and all partial derivates are continuous

  1. #1
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    ODE-Determining whether differential and all partial derivates are continuous

    Please help!
    I have been given the condition:
    U is a ball of radius r>0 in R^n, it is centred at a.
    x is an element in U given length (x-a)<r
    The ordinary differential equation:
    dx/dt = v(t,x),
    where x=(x1, x2, ..., xn)^T is an element in R^n.
    If U is continuous and all partial derivatives are continuous in U. Let |t-t0)<T, then dx/dt=v(t,x) has a unique solution satisfying x(t0)=a defined on interval J which is part of R.
    Determine whether the following equations satisfy the above condition:
    (a): dx/dt=Ax^(1/2), where A is a constant
    (b): dx/dt=x^2

    Any help on proving whether the equations satisfy this condition will be VERY appreciated, or even just some information on the topic/process that will be helpful!
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  2. #2
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    Re: ODE-Determining whether differential and all partial derivates are continuous

    Mark joy wont be too happy if he sees this.
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