Is there any easy way to solve matrix differential equation?

i.e. i want to solve dp/dt = ip , where p is a matrix .

(my main problem is to solve solve dp/dt = ip + L(p) , where L is the liouvillian of an operator)

thank you in advance

[Babak]

What's the dimension of the matrix p?

Is i a constant?

[Nikolaos]

Usually the dimensions are 36x36 of p . i is just imaginary constant number. L is an operator that involves a sum of matrices.

Answer 1

[Babak]

The analytical solution to the problem of dp/dt = ip is

p(t) = C exp(it)

where C is a constant matrix same size as p used to determine the initial condition. i can be either a scalar or a matrix. If i is a matrix, in the above solution exp(it) will be a matrix as well which is defined in the literature.