The system of differential equations in the last worksheet was "uncoupled." That is, x did not affect the way y changed, and the change in a was not affected by y. However, in general, there could be interaction between x and y such that the rate of change of a depends on both x and y, and similarly, the rate of change of y depends on both x and y. A "coupled" system of linear differential equations can be described by dx dt = ax + by dy dt = cx + dy. This system can be written in matrix/vector form as d at Ly A Ly where A [ 2 2] The result that we found for the uncoupled system can be generalized to (just about) any system of linear differential equations. That is, we can write the general solution to a linear system of differential equations (in vector form) as (1) where 1 and 12 are the of the matrix of coefficients A, and 01 = and 12 = V21 V12 122 are the of A. The arbitrary constants c2 and c2 are determined when initial conditions are applied. (Compare this solution to the solution for the uncoupled system.) 1. Fill in the blanks above