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10 Nov 2019
In this question, we will discuss the stability of the equilibrium solutions of y' = f(y) = (y- 1)2y(y + 1): Sketch the graph of f(y) versus y. Determine all the critical (equilibrium) points, and classify each as asymptotically stable, unstable or semistable. Draw the phase line, and sketch several graphs of solutions in the ty-plane. In this question, we will try to use the exact equation method to solve the DE: sin(xy)/x + y cos(xy) + x cos(xy)y' = 0 Check that the differential equation is not exact. Find the integration factor mu which makes it exact. Using mu, solve the differential equation.
In this question, we will discuss the stability of the equilibrium solutions of y' = f(y) = (y- 1)2y(y + 1): Sketch the graph of f(y) versus y. Determine all the critical (equilibrium) points, and classify each as asymptotically stable, unstable or semistable. Draw the phase line, and sketch several graphs of solutions in the ty-plane. In this question, we will try to use the exact equation method to solve the DE: sin(xy)/x + y cos(xy) + x cos(xy)y' = 0 Check that the differential equation is not exact. Find the integration factor mu which makes it exact. Using mu, solve the differential equation.