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Math Help - differentiation with repsect to time

  1. #1
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    differentiation with repsect to time

    Hi,

    How do i express this in terms of t?

    a dv/dt = -g/b2(v(t)^2 + b^2)
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    if you mean

    \frac{dv}{dt}=\frac{-b}{g}(v^2+b^2)..this is an SDE...
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  3. #3
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    SDE? New to this thing!
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  4. #4
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    the initial part should have said express t in terms of v,b,g, and vo(the initial speed of the ball).
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  5. #5
    MHF Contributor Mathstud28's Avatar
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    Yes

    SDE stands for seperable differential equation? seperate variables...integrate...solve for t...make sense? if not reply and I will try to walk you through it
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  6. #6
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    i would appreciate the help thankyou!
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  7. #7
    MHF Contributor Mathstud28's Avatar
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    Ok here is what you have to do

    I will give you an example \frac{dy}{dx}=9y^4..seperate so that all the ys are with the dys and all the dxs are with the xs...so we have then that \frac{dy}{y^4}=9dx...now we want to get rid of the dx's and dy's...so we integrate \int\frac{dy}{y^4}=\int{9dx}...so we get \frac{-1}{3y^3}=9x+C...now since y is a function of x to we are trying to find y like you are trying to find v...so we solve for y y^3=\frac{-1}{27x+C_1}.... y=\frac{-1}{(27x+C_1)^{\frac{1}{3}}}..now that is an SDE...now reevaluating this...can you tell me if this an SDE?
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  8. #8
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    think i understand so I have to take all the variables relating to t on to the left hand side of the equation and leave the other variables on the right hand side of the equation??

    A(t)/v(t)^2 = (-g/b^2)*b^2


    ??????
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  9. #9
    MHF Contributor Mathstud28's Avatar
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    No

    You are looking at this too much from a physics perspective...forget that a(t)=\frac{dv}{dt} leave it as it is seperate and integrate then solve...but make sure its an SDE
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  10. #10
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    sorry but im confused now because my question begins with by writing a = v dv/dx ........

    also why dont the constants stay together on the right hand side? Or have i misunderstood the criteria for the equation?
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  11. #11
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    can some one check this answer please?

    dv/dt = -g/b2(v(t)^2 + b^2)

    separation of variables

    1/v(t)^2 + b^2 = -g/b2

    Integration

    1/b^2arctan(v(t)^2/b^2) = ln(-g + b^2)+c


    I think its totally wrong so any help would be appreciated!
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