Hello everyone!

I'm unable to solve this differential equation while solving a physics question. So please help me in solving this equation:

$m\frac{dv}{dt}=mg -\lambda\frac{v}{x(x-d)}$ or

$m\frac{vdv}{dx}=mg-\lambda \frac {v }{x(x-d)}.$

$UPDATE$:

$Here$ $I$ $want$ $to$ $express$ $either$

$v=f(t)$

or

$v=f(x)$.

$Given$.

where all terms have the usual meaning:

'$\lambda$' is constant.

$v$ is the velocity of the rod (variable)

$m$ is the mass of the rod (constant)

$x$ is the distance from a fixed point to the rod (variable)

$t$ is time (obviously a variable)

and $d$ is the intial distance (constant)

$Note$:

This is a part of a question that I'm writing. I'm unable to proceed further because of this difficult differential equation.

Please help! Thanks.

**UPDATE**

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## Comments

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TopNewestIn the first equation multiply both sides by differential $dt$.Also write $v = \frac {dx}{dt}$.

You should get : $mdv = mgdt - \frac {\lambda dx}{x(x-d)}$

You also need to know three initial conditions : Initial time which is $0$,initial position and initial velocity.

Did I make a mistake in doing this?

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Yes i did it in same way...!!

But I want to express velocity as either $v=f(t)$ or $v=f(x)$ so that further question is completed. Since Both time and distance are different. I mean to say if I want to calculate say velocity at the instant say at t=10 s then how could I know velocity at that instant since position is also unkown at that instant of Time. ?? and Also according to this question $v = \frac {d(x-d)}{dt}$. which is also same thing as $v = \frac {dx}{dt}$.

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I believe the differential equation is not meant to be solved by wolfram alpha itself.

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@Ronak Agarwal @jatin yadav will you help ??

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@Pranav Arora @Finn Hulse any Help??

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I don't think I'll be of much help on the problem, but certainly the LaTeX needed editing. Is this the way you would like it to appear?

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$v=f(x)$ or $v=f(t)$.?? which is essential for this question. ( that is my Problem)

Thanks,@Finn But how can I expressedLog in to reply

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$v$? Because if you are, I think it would be very tricky.

Are you asking if you can solve forLog in to reply

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"$padharo$ $mhare$ $desh$"

Well for what purpose you have been come here... is it Vacation's celebration or something else ?

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@Calvin Lin sir @Michael Mendrin sir any help??

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Can you please post that whole physics question itself on which you are working.

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@Ronak Agarwal Ok Done it. You can check it Here.

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Hi Deepanshu please try this question. I think you will find this interesting.

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@satvik pandey Done..!!

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