Draw a direction field for the differential equation y' = -y(10 - y). Based on the direction field, determine the behavior of y as t → ∞. If this behavior depends on the initial value of y at t = 0, describe this dependency. The two equilibrium solutions are y(t): and y(t) = Solutions with initial values greater than 10 Choose one ▾ Solutions with initial values between 0 and 10 Choose one ▾ Solutions with initial values less than 0 Choose one ▾ =

For the Attached problem, Identify the equilibrium values. Which are stable and which are unstable? Construct a phase line. Identify the signs of and Sketch several solution curves

A force of 660 newtons stretches a spring 3 meters. A mass of 55 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 12 m/s. Give the initial conditions. x(0) = x'(0) = Find the equation of motion. x(t) =

Plot the phaseportrait and characterize the equilibrium.