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Method of the characteristics

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Hi.
I have some questions of (PDEs). I have attached the document in attachments.

But, please the solution must has the solutions' steps.

Note: the first question has simple change(See that in attachements )

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Solution Summary

Method of the characteristics to solve is employed.

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(1) Solution:
Using method

From last term, u = c (constant.)
From second term, t = s + d (constant)
From first equation and using u = c, we have
x = 3c s + e (constant) => x = us + e
We assume at t = 0, s = 0, then d =0
Thus s = t,
Then x = us + e => x = 3ut + e
 e = x - ut
 u = c = f(e) = ...

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