Hi, I need help solving these problems below. I am not sure how to approach these questions, so requesting kindly if work and process is shown. Thank you.

1) Solve the following initial value problem, leaving your solution in implicit form. y' = my +4x y(0) =2 2) Suppose the population of a certain species was governed by the following differential equation: dP - 4p-P . dt where / is in years, and P is population in thousands (e.g., P = 3.5 would mean a population of 3500). a) Find the carrying capacity. b) Suppose the growth pattern changed so that the model became dt -=4p-p: -3. What is now influencing the population? Explain. c) Find the general solution of the differential equation in (b), leaving your answer in implicit form. d) Now, solve for an explicit form of your solution; call it P(). e) Use your solution from (d) to compute lim P() (This will yield a new "carrying capacity.") 3) The following equations represent a predator-prey system: dx dt -=0.1x -0.004xy -0.01x dy dt = -0.2y+0.003xy +100 a) Which variable represents the predator population? Which represents that of the prey? b) Is there competition within one of the species? If so, which one? c) Is one of the species experiencing immigration or emigration (harvesting)? If so, which one of these and for which population