Given dy/dx = y^2 − 4y + 4 (a) Sketch the phase line (portrait) and classify...

Given dy/dx = y^2 − 4y + 4

(a) Sketch the phase line (portrait) and classify all of the critical (equilibrium) points. Use arrows to indicated the flow on the phase line (away or towards a critical point).

(b) Next to your phase line, sketch the graph of solutions satisfying the initial conditions: y(0)=0, y(0)=1, y(0)=2, y(0)=3, y(0)=4.

(d) State the solution to the initial-value problem dy/dx = y^2 − 4y + 4, y(0) = 2.

Solutions

Expert Solution

If you have any doubts in the solution please ask me in comments...

In first part i draw phase line

Second part i draw direction field then i draw solution curve with help of direction field

Third we simply use curve for limit

In 4 we find y=2 is singular slolution

Colby Messinger answered 1 year ago

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