Given the differential equation y' = y^4 - y^2       (notation: y^n means "y to the n-th power") (a) Find all equilibrium solutions. (b) Determine the stability of each equilibrium solution (c) Is the solution through the point (0, 2) unique? Justify your "YES" or "NO" answer with a one line argument. An answer "YES" or "NO" will get no credit. (d) solve the differential equation.

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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.