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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.

Attachment 23674

hints?

Re: System of PDE's found in GR (8 hours, fustrated)

Since you are differentiating both x and t with respect to $\displaystyle \alpha$, it is clear that x and t are to be functions of $\displaystyle \alpha$. However, these are NOT "PDE"s because you are taking the two functions, x and t, to depend on the one variable, $\displaystyle \alpha$. What you have is a system of second order **ordinary** equations.

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.

Re: System of PDE's found in GR (8 hours, fustrated)

Quote:

Originally Posted by

**Flamingpope** 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.