Determine a region of the xy-plane for which the given differential equation has

Question

Determine a region of the xy-plane for which the given differential equation has a unique solution passing through a point (x0- yo) in the region. x(y - 3)y' = 1 Use computer software to obtain a direction field for the given differential equation. By hand, sketch approximate solution curves that pass through the points (1. 2), (0. 0), and (2, 3). y' = 2 - x - y Find the critical points and phase portrait of the given autonomous first-order differential equation. Classify each critical point as asymptotically stable, unstable, or semi-stable. By hand, sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions. dx / dt =x(x- 1)(x + 1)

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