Sketch the phase portrait for the competing species system: y'1 = y1(1 − y1 − 2y2) y'2 = y2(1 − y2 − 2y1) In particular, for full credit you must show the equilibrium points, nullclines, and some representative trajectories. Based on your phase diagram, what will happen to the populations of the two species in the long term?

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A: SOLUTION-

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Q: Exercise 1.5.5: Solve y' = (x + y − 1)². -

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.