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Math Help - Characteristics - assosciated ODEs - how do you show this?

  1. #1
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    Characteristics - assosciated ODEs - how do you show this?

    How do you show that if you have the assosciated ODEs of a pde:

    dx/a = dy/b = dz/c = ds,

    then for constants m,n,p

    it is also true that

    (mdx + ndy + pdz)/(ma + mb + pc) = ds?
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  2. #2
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    If dx = a ds, dy = b ds, dz = c ds  then m dx = m a ds, n dy = n b ds, p dz = p c ds.

    Adding gives

    m dx + n dy + p dz = (m a + n b + p c)ds and dividing gives your answer
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