Please solve the following numerical analysis problem:
Determine the flow Qt : R^2 into R^2 for the nonlinear system: x' =f(x) with
f(x) = [ -x1 ]
[ x1^2 + 2x2 ]
and show that the set S = { x E R^2l x2 = -x^2/4 } is invariant with respect to the flow {Qt}.
Please use the step by step method to show the solution.