# Thread: Characteristics - assosciated ODEs - how do you show this?

1. ## 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?

2. If $dx = a ds, dy = b ds, dz = c ds$ then $m dx = m a ds, n dy = n b ds, p dz = p c ds$.

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