1. A direction field for the differential equation $y' = x cos pi y$ is shown. (a) Sketch the graphs of the solutions that satisfy the given initial conditions. (i) $y(0) = 0$ (ii) $y(0) = 0.5$ (iii) $y(0) = 1$ (iv) $y(0) = 1.6$ (b) Find all the equilibrium solutions.
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(i) For y(0) = 0, the initial point is (0, 0). Following the direction field, the solution curve starts at the origin and moves along the arrows. The curve will have a sinusoidal shape, oscillating between positive and negative values of y. (ii) For y(0) = 0.5, Show more…
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