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 Differential Equations Ordinary and Partial Differential Equations Math Forum

January 30th, 2012, 03:59 AM   #11
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Re:

Quote:
Originally Posted by skipjack
Quote:
 Originally Posted by Taurai Mabhena am I to assume that skipjack's FULL answer . . .
No.

But why would the last term be left out i.e why
$\dot{x}= \frac{dx}{dt} = \frac{\partial x}{\partial y} \dot{y} + \frac{\partial x}{\partial z} \dot{z}$
and NOT
$\dot{x}= \frac{dx}{dt} = \frac{\partial x}{\partial y} \dot{y} + \frac{\partial x}{\partial z} \dot{z} + \frac{\partial x}{\partial t}$

I would have thought that adding the last term $\frac{\partial x}{\partial t}$ allows for x to explicitly vary with time t.

 January 30th, 2012, 02:55 PM #12 Global Moderator   Joined: Dec 2006 Posts: 20,476 Thanks: 2039 I originally gave "x is a function of y and z". Perhaps I should have given "x is a function of y and z only" so as to make it clearer that x is not explicitly a function of t as well as y and z.

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