Consider the differential equation:  (dy/dx) = (e-y/x2) , x > 1/2  1. Find the general solution of the differential equation explicitly in the form y = f (x).  2. Find the particular solution that satisfies y (1)

The population of fish in a lake grows logistically according to the differential equation where t is in years with no harvesting. If the lake has 550 fish and opens to fishing, determine how many fish can be harvested per year to maintain equilibrium. dy/dt=0.1y(1-y/2500) Differential Equations

Let (a) (b) (√x+²) dx + (y² + In(2x)) dy=0, x>0. Check that this is an exact differential equation. Solve the equation leaving the general solution in implicit form.