I have a system that is defined as follows:
$\dot{x}(t) = Ax(t) + Bu(t),\quad\quad x(0)=x_0.$
It has a well known solution:
$x(t) = e^{tA}x_{0} + \int_0^t \! e^{(t-\tau)A}Bu(\tau) \, \mathrm{d}\tau $
I know that one of the tasks during exam will be to draw the the graph of the solution given that A and B are numbers. If B is zero then this is no problem, but if it's not I don't really know how to calculate that integral. Could anyone please explain the steps that I need to perform to solve this?
PS> I've already found some examples but none of them showed the intermediate steps, so I can't figure out anything :/