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Math Help - Integrating factor and differential equation questions help

  1. #1
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    Integrating factor and differential equation questions help

    Q1.
    A skydiver’s vertical velocity v is governed by the differential equation:
    m
    dv
    dt = mg − Kv2
    where m is the mass of the skydiver, g is the gravitational constant, and K > 0
    is the drag coefficient. If the skydiver leaves the airplane at time t = 0 with zero
    vertical velocity, find at what time she reaches half her final velocity

    Q2.
    Solve the following problems by finding an integrating factor:
    (a) dx/dt + 2x = e^−4t
    (b) dx/dt −x/t = t^3 − 3, x(1) = −1
    (c) t(dx/dt) + 4x = e^t

    Any help or explanation would be appreciated. I have very little of an idea of how to approach these questions.
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  2. #2
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    Re: Integrating factor and differential equation questions help

    I can't read your first equation. Is it \displaystyle \frac{dv}{dt} = m\,g - k\,v^2 ?

    As for question 2, they all follow the same procedure. Do you understand how to find an integrating factor and use it to simplify a DE?
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  3. #3
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    Re: Integrating factor and differential equation questions help

    Hi, sorry it's m(dv/dt) = mg - kv^2. And no, I basically dont understand how to use the integrating factor
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