Differential Equation Question

Question

How would I write this in matrix form (x' = AX) 

 

x' = x

y' = y

 

Note: Is it supposed to be like this: x' = (1 v 1)(x v y) or x' = (1 + 0 v 1 + 0)(x v y)? Note: the "v" means the value after it goes below.

Answer 1

[X'] will be a 2-by-1 vector with components [x' y'], and [X] will be the 2-by-1 vector [x y]. 

 

[A] is a 2-by-2 matrix of coefficients determined by the differential equations:

 

x' = 1x + 0y

y' = 0x + 1y

 

[x'] = [1 0] [x]

[y'] = [0 1] [y]