Solve the first order hyperbolic equation

  • Thread starter andrey21
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  • #26
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So

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

So

log u = x2/3 + log (2r+4) - r2/3
 
  • #27
hunt_mat
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Yey, and now you know what r in terms of t and x are, substitute these in and you will have your solution.
 
  • #28
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So:

t = x2 /3 - r2 /3

r2 /3 = x2 /3-t

r2 = x2 -3t

r = SQRT (x2 -3t)
 
  • #29
hunt_mat
Homework Helper
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Good so far, remember there is an associated [itex]\pm[/itex] along with the answer. You have to decide which it is, but this shouldn't be too hard.
 
  • #30
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So :

r = [itex]\pm[/itex]SQRT (x2 -3t)

What is the next step?
 
  • #31
hunt_mat
Homework Helper
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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!!
 
  • #32
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Which equation shall I plug the r value into?

Is it:

log u = x2/3 + log (2r+4) - r2/3
 
  • #33
hunt_mat
Homework Helper
1,745
26
Yes.
 

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