# Solve the first order hyperbolic equation

So

c= log (2r+4) - r2/3

So

log u = x2/3 + log (2r+4) - r2/3

hunt_mat
Homework Helper
Yey, and now you know what r in terms of t and x are, substitute these in and you will have your solution.

So:

t = x2 /3 - r2 /3

r2 /3 = x2 /3-t

r2 = x2 -3t

r = SQRT (x2 -3t)

hunt_mat
Homework Helper
Good so far, remember there is an associated $\pm$ along with the answer. You have to decide which it is, but this shouldn't be too hard.

So :

r = $\pm$SQRT (x2 -3t)

What is the next step?

hunt_mat
Homework Helper
Plug it in and see what sign causes you trouble (I think it'll be the - sign that will be the troublesome one). Look for large values of x to find the right sign. Then you're done, you've got the right solution!!

Which equation shall I plug the r value into?

Is it:

log u = x2/3 + log (2r+4) - r2/3

hunt_mat
Homework Helper
Yes.