- #1
cris(c)
- 26
- 0
Homework Statement
Hi everyone,
Consider the following system of (first order) differential equations:
[itex]\dot{x}=f(t_1,x,y,z) [/itex]
[itex]\dot{y}=g(t_2,x,y,z) [/itex]
[itex]\dot{z}=h(t_3,x,y,z) [/itex]
where [itex]\dot{x}=\frac{\partial x}{\partial t_1}[/itex], [itex]\dot{y}=\frac{\partial y}{\partial t_2}[/itex], and [itex]\dot{z}=\frac{\partial z}{\partial t_3}[/itex].
Homework Equations
All existence theorems I know (picard and peano) are formulated such that [itex]t_1=t_2=t_3[/itex], but I'd like to know how to extend these results to the cae shown above.
The Attempt at a Solution
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 [itex]t_1 \neq t_2 \neq t_3[/itex]? Any help/reference where to look for such theorem would be greatly appreciate!