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    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?

    © BrainMass Inc. brainmass.com February 24, 2021, 2:33 pm ad1c9bdddf
    https://brainmass.com/math/ordinary-differential-equations/first-order-ordinary-differential-equations-28591

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