Are these partial or ordinary differential equations?

[cris(c)]

Homework Statement

Consider the following system of (first order) differential equations:
$\dot{x}=f(t_1,x,y,z)$
$\dot{y}=g(t_2,x,y,z)$
$\dot{z}=h(t_3,x,y,z)$

where $\dot{x}=\frac{\partial x}{\partial t_1}$, $\dot{y}=\frac{\partial y}{\partial t_2}$, and $\dot{z}=\frac{\partial z}{\partial t_3}$.

Homework Equations

Is this a system of partial differential equations?

The Attempt at a Solution

I believe it is because there are more than one 'independent' variable. But I am not quite sure of this...

 

[mighty2000]

You are correct, this is a system of partial differential equations. The presence of multiple independent variables, in this case t1, t2, and t3, is what makes it a partial differential equation. In contrast, a system of ordinary differential equations would only have one independent variable.

The notation \dot{x}, \dot{y}, and \dot{z} also indicates that these are first order derivatives with respect to their respective independent variables. This further confirms that it is a system of partial differential equations.

I hope this helps clarify your understanding. Good luck with your studies!



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