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Having the Hardest Time

  1. Feb 11, 2005 #1
    I know at some point, years ago, I could differential equations in my sleep. But now after going through my old math book and reading a number of the threads here, I'm really confused. The problem I am looking to solve looks like this:

    [itex]
    dV = - \mu V^2 t - \beta t
    [/itex]

    where mu and beta are constants, t is time and V is horizontal velocity. I want to compute the horizontal velocity at time t given the initial horizontal velocity, mu and beta. My problem gets more complex with the second equation I need to solve:

    [itex]
    dH = \gamma V^2 t - \alpha t
    [/itex]

    where gamma and alpha are constants, t is time, V is horizontal velocity and H is vertical velocity. I want to compute the vertical velocity at time t given the initial horizontal velocity. I've been going nuts trying to make this work in my head. They look like rudimentary textbook problems, but I just can't seem to make sense of them. Could someone walk me through the steps?
     
  2. jcsd
  3. Feb 11, 2005 #2

    dextercioby

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    In both equations the "dt" is missing.I can assume it should be in the RHS,case in which i would advise you to integrate directly both sides of the equations...

    Daniel.
     
  4. Feb 11, 2005 #3

    mathwonk

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    yes, the basic rule is balance units: i.e. if one side is a differential, the other is too.
     
  5. Feb 11, 2005 #4
    Oops. Sorry, the t should have been dt. Corrected:

    [itex]
    dV = - \mu V^2 dt - \beta dt
    [/itex]

    [itex]
    dH = \gamma V^2 dt - \alpha dt
    [/itex]

    So, how do I integrate these? Let's take the first one and divide by dt. Then I get:

    [itex]
    \frac {dV} {dt} = - \mu V^2 - \beta
    [/itex]

    Now what...
     
  6. Feb 11, 2005 #5

    dextercioby

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    You needn't have done that.U already had separated variables and u only had to integrate.

    Daniel.
     
  7. Feb 11, 2005 #6

    dextercioby

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    EDIT:You've changed your equations a great deal and now the advice goes:SEPARATE VARIABLES...

    Daniel.
     
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