Population model

In some populations, the amount of births is directly proportional to the population at any given point in time and the amount of deaths is directly proportional to the square of the population at any given point in time. 1. Write an equation that models the change in a population that fits the above description. Make sure to carefully label what each variable represents. 2. Your equation from (1) should be separable. Separate the equation by hand but use your TI calculator to perform the appropriate integration (don’t forget the constant of integration). Then use the solve function to solve this equation for the population. 3. Use the deSolve function to solve your original equa... click for more

Differentiation

Consider the differnetial equation y'(x) + xy(x) = 0 with y(0) = 0 Look for a solution of this problem of the form y(x) = A + B + Ce^-x + De^-1/2x^2 Use the fact that y must satisfy the equation and the initial conditions to indentify the constants A,B,C and D. By setting u = -x^2/2 in the power series for f(u) = exp{u}, determine a power series for y(x). What is the radius of convergence of the power series for y(x)? I am having trouble in grasping the whole concept of this problem. Can anyone help. Thanks

Mathematical Modelling

Simulation

A skydiver, weighing 70kg, jumps from an aeroplane at an altitude of 700 metres and falls for (T) seconds before pulling the rip cord of his parachute. A landing is said to gentle if the velocity on impact is no more than the impact velocity of an object dropped from a height of 6 metres. The distance that the skydiver falls during (t) seconds can be found from Newton's Second Law, F = ma. During the free fall portion of the jump, we will assume that here is essentially no air resistance, so F = -mg, where g = 9.8m/s and m = 70kg. After the parachute opens, a significant drag term due to air resistance of the parachute affects the force (F), causing the force to become F = -mg - kv, wh... click for more

Product rule and chain rule

I have done most of the calculations but require confirmation.