 Solution

ID: past-exam-of-the-algebra-1-and-differential-equations-1-course-of-the-university-of-oxford/2015/4/a/i/solution

An autonomous differential equation has no explicit dependence on the independent time variable: its vector field depends only on the current state. The two families of nullclines are

X (x, y) = 0 and Y (x, y) = 0.

On the first family the horizontal velocity is zero; on the second the vertical velocity is zero. A critical point of a dynamical system is a state where both components vanish. It gives a constant solution, also called an equilibrium.

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