suppose I have "n" coupled differential equation represented by the matrix,
Y• = A Y, where Y• is the column matrix containing first derivatives, namely, y1•(t), y2•(t), ... yn•(t) . A is a square matrix whose each element contains some function dependent on "t" (not constants) and Y is the column matrix containing the solution set, namely, y1(t), y2(t), ... yn(t) .
If A, contained constants, then its easy to solve by Matrix Exponential method or Eigen-Value method. But, if it contains some varying functions, then is there any approach to solve this. Please, direct me to a good reference, if possible, with an example.