# First order ordinary differential equations

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Problem A:

Suppose that a giant HD-ready television of mass m falls from rest towards earth and its parachute opens at time t=0. when its speed is v(0)=v0

Since the TV is massive assume the drag force is proportional to the square of the velocity.

Write a complete model for the velocity v(t)

What is the asymptotic behavior of the solution as t approaches infinity.

Problem B:

Solve the initial value problem y'=y^2 y(0)=2

Whet is the largest interval of existence?

Problem C:

Recall the Verhulst model for a population P(t)

P'=aP-bP^2 for a>0 and b>0

1. Whet kind of equation is it?

2. Solve using change of variables z = 1/P

3. What is the asymptotic behavior of P?

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