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First order ordinary differential equations

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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The 9 pages attachment explicitly details the full method top answer the problems.

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