[a] The equilibrium solutions of a certain DE = f(y) (where f(y) is a continuous function) are y= 2, y=6 and y=-3. y = 2

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A The Equilibrium Solutions Of A Certain De F Y Where F Y Is A Continuous Function Are Y 2 Y 6 And Y 3 Y 2 1 (54.87 KiB) Viewed 20 times

[a] The equilibrium solutions of a certain DE = f(y) (where f(y) is a continuous function) are y= 2, y=6 and y=-3. y = 2 is a semi-stable equilibrium solution, y = 6 is an unstable equilibrium solution and f(-5)=9. Draw the phase portrait for the DE as shown in lecture. Sketch a possible graph of f(y) (the horizontal axis is y, the vertical axis is f(y)). Label relevant points on the horizontal axis. Do not try to find a formula for f(y). You will graded only on the general position of your graph. [] [c] Find the following limits for the given initial value problems. If = f(y), y(8)=1 find lim y(x) If y = f(y), y(-2) = 3 find lim y(x) [d] Is y=-3 a stable, unstable or semi-stable equilibrium solution ?