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p3forlife
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Homework Statement
Describe the phase portrait of the nonlinear system x' = x^2, y' = y^2
Also, find the equilibrium points and describe the behaviour of the associated linearized system.
The Attempt at a Solution
We have an equilibrium point at (0,0).
The associated linearized system is x' = 0, y' = 0. The phase portrait for this consists of lines of equilibria along x = 0, and y = 0.
For the nonlinear system, I have found solutions x(t) = -1/t and y(t) = -1/t. I don't know what these solutions mean in terms of a phase portrait. Nor can I express the solutions in terms of constants x_0 and y_0.