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Math Help - System of PDE's found in GR (8 hours, fustrated)

  1. #1
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    Angry System of PDE's found in GR (8 hours, fustrated)

    Yes it's GR - but a good portion of funds goes towards solutions to these kinda things.
    This one noted as particularly *easy* by a professor, so I would like some hints with this one on methods of solving.

    How should I go about solving for t in terms of alpha? or alpha in terms of t? (no dependence on x)
    The solution I heard is actually in the form of an integral.
    System of PDE's found in GR (8 hours, fustrated)-problem.jpg
    hints?
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  2. #2
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    Re: System of PDE's found in GR (8 hours, fustrated)

    Since you are differentiating both x and t with respect to \alpha, it is clear that x and t are to be functions of \alpha. However, these are NOT "PDE"s because you are taking the two functions, x and t, to depend on the one variable, \alpha. What you have is a system of second order ordinary equations.
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    Re: System of PDE's found in GR (8 hours, fustrated)

    Agreed on mistake - it is indeed ordinary, and there was of course another way to approach the problem. Still a nasty transcendental of logs and trigs it turns out.
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    Re: System of PDE's found in GR (8 hours, fustrated)

    Quote Originally Posted by Flamingpope View Post
    Agreed on mistake - it is indeed ordinary, and there was of course another way to approach the problem. Still a nasty transcendental of logs and trigs it turns out.
    Could you show us. I couldn't get to the point of the solution. The best I could do was to reduce the problem to a first order ODE.
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