In general if dy/dx = f(y)

Then the steady state solutions are the zeroes of f(y)

Let a =alpha

For dN/dt = rN(1-aN) - h

Steady states are found when rN(1-aN) - h = 0

Expanding -arN^2 + rN - h = 0

Use the good ol' quadratic formula

N = 1/2a+sqrt(r^2 - 4arh)/2ar

this will clean up to 1/2a+sqrt(1-4ah/r)/2a

or N = [1+sqrt(1-4ah/r)]/2a

since r > 4ah the solutions are real

By considering a graph of dN/dt vs N you should be able to determine N1 unstable and N2 stable

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