- #1
adamjts
- 24
- 0
Hi I'm just having trouble wrapping my head around differential equations with matrices and vectors...
For example:
let y be a vector.
let A(t) be an nxn matrix.
I have the differential equation:
dy/dt = A(t)y
So I think I understand why the solution is
y = ceA(t)
But I'm having trouble understanding how to actually get information from this. For example, if someone asked be to find the yi component at some time t, I wouldn't know how to do it. My friend told me to think of the as a taylor expansion, but I'm still not entirely understanding how to do this. Can someone help explain?
For example:
let y be a vector.
let A(t) be an nxn matrix.
I have the differential equation:
dy/dt = A(t)y
So I think I understand why the solution is
y = ceA(t)
But I'm having trouble understanding how to actually get information from this. For example, if someone asked be to find the yi component at some time t, I wouldn't know how to do it. My friend told me to think of the as a taylor expansion, but I'm still not entirely understanding how to do this. Can someone help explain?