# Non-linear ODE from closed-loop system and Response (Part II)

I again need help with the Mathematica. We have the following affine system. I need to get expressions describing the changes of $$x_{1} \left( t \right)$$ or $$x_{2} \left( t \right)$$. The only thing that turned out to me was to build a numerical representation on the graph. 1. What command is used in Maple to get the equation of the desired output variable? I tried using the Extract command, but as an answer, the math showed just "$$x_{1} \left( t \right)$$"; 2. It is seen that the ODE is essentially nonlinear. How to present in Math not necessarily an exact solution, but at least in the form of a series at a specified time interval?

There is my code:

asys = AffineStateSpaceModel[{Subscript[x, 1]'[
t] == (Power[Subscript[x, 1][t], 2] +
Power[Subscript[x, 2][t], 2]) 0.2 Sin[4 t] - 0.2 Cos[4 t] +
Subscript[u, 1][t],
Subscript[x, 2]'[
t] == (Power[Subscript[x, 1][t], 2] +
Power[Subscript[x, 2][t], 2]) 0.3 Sin[5 t] - 0.3 Cos[5 t] +
Subscript[u, 2][t]}, {Subscript[x, 1][t],
Subscript[x, 2][t]}, {Subscript[u, 1][t],
Subscript[u, 2][t]}, {Subscript[x, 1][t], Subscript[x, 2][t]}, t]

Plot[OutputResponse[{asys, -1}, {0, 0}, {t, 0, 500}] // Evaluate, {t,
0, 500}]