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

• Apr 21st 2012, 10:33 AM
Flamingpope
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?
• Apr 24th 2012, 03:43 PM
HallsofIvy
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.
• Apr 25th 2012, 01:39 PM
Flamingpope
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.
• Apr 27th 2012, 09:53 AM
Jester
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.