Prove that if a trajectory starts at a noncritical point
Question and Solution
Prove that if a trajectory starts at a noncritical point of the system dx dt = F(x, y), dy dt = G(x, y), then it cannot
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Prove that if a trajectory starts at a noncritical point of the system dx dt = F(x, y), dy dt = G(x, y), then it cannot reach a critical point (x0, y0) in a finite length of time. Hint: Assume the contrary, that is, assume that the solution x = ?(t), y = ?(t) satisfies ?(a) = x0, ?(a) = y0. Then use the fact that x = x0, y = y0 is a solution of the given system satisfying the initial condition x = x0, y = y0 at t = a.
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