it's calculus2

1. Find the general solution of the differential equation. Write your solution explicitly. y" = {y2 + 3:2 05202 2. Consider the initial value problem dy_ 2 _ d, y 5y+6.y(0)1 where y represents the population of a species (in thousands), and t represents time (in years). a} Solve this initial value problem to nd the population as a function of time. Write your solution explicitly. b) What number does the population approach in the long term? (i.e., nd an equilibrium solution by computing ELIE y(t)) c} What number would the population approach if one could, theoretically, go back in time? (i.e., nd an equilibrium solution by computing 39100 thD. 3. Consider the parametric equations x = t3 121' + 1,}? = 2t 132. a) Find the slope of the tangent line at I = -1. b) Find the points where the tangent is vertical or horizontal