Hi I'm just having trouble wrapping my head around differential equations with matrices and vectors...(adsbygoogle = window.adsbygoogle || []).push({});

For example:

letybe 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= ce^{A(t)}

But I'm having trouble understanding how to actually get information from this. For example, if someone asked be to find the y_{i}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?

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# I Conceptual Question: Vector-Matrix Differential Equation

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