# System of ODE

1. Jan 2, 2012

### cris(c)

Hi everyone,

I'm not quite sure how to proceed to show existence (and perhaps uniqueness) of 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 $\dot{z}=\frac{\partial z}{\partial t_3}$.

All existence theorems I've seen are formulated such that $t_1=t_2=t_3$. I've tried reading the proofs to see if I can figure out a way to apply them to this problem, but I can't see how...Does someone knows whether these theorems hold true when $t_1 \neq t_2 \neq t_3$? Any help/reference where to look for such theorem would be greatly appreciate!!!