In each of the following cases, we define a function
:
$\phi$: ${\mathbb R} \times {\mathbb R}^3 \rightarrow {\mathbb R}^3 $
. Determine in
each case whether this function could be the flow of a differential equation, and write
down the differential equation.
(a) $\phi_t(\vec{x}) = \vec{x} = (8,1,0)$,
(b) $\phi_t(\vec{x}) = \vec{x} = \vec{x} \ \text{for all } t, $
(c) $\phi_t(\vec{x}) = \vec{x} + (t,t,t).$
Could anyone helps me to decide how to determine the flow of a differential equation as I have trouble understanding what is the flow of a differential equation, and write down the differential equations?
:
$\phi$: ${\mathbb R} \times {\mathbb R}^3 \rightarrow {\mathbb R}^3 $
. Determine in
each case whether this function could be the flow of a differential equation, and write
down the differential equation.
(a) $\phi_t(\vec{x}) = \vec{x} = (8,1,0)$,
(b) $\phi_t(\vec{x}) = \vec{x} = \vec{x} \ \text{for all } t, $
(c) $\phi_t(\vec{x}) = \vec{x} + (t,t,t).$
Could anyone helps me to decide how to determine the flow of a differential equation as I have trouble understanding what is the flow of a differential equation, and write down the differential equations?
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