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**

Click here to get full Question Click Here.

## 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? – Arif Ahmed · 2 years, 7 months ago

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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 \(v = \frac {dx}{dt}\). – Deepanshu Gupta · 2 years, 7 months ago

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– Ronak Agarwal · 2 years, 7 months ago

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

Hi Deepanshu please try this question. I think you will find this interesting. – Satvik Pandey · 2 years, 7 months ago

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@satvik pandey Done..!! – Deepanshu Gupta · 2 years, 7 months ago

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Can you please post that whole physics question itself on which you are working. – Ronak Agarwal · 2 years, 7 months ago

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@Ronak Agarwal Ok Done it. You can check it Here. – Deepanshu Gupta · 2 years, 7 months ago

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@Ronak Agarwal @jatin yadav will you help ?? – Deepanshu Gupta · 2 years, 7 months ago

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@Calvin Lin sir @Michael Mendrin sir any help?? – Deepanshu Gupta · 2 years, 7 months ago

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@Pranav Arora @Finn Hulse any Help?? – Deepanshu Gupta · 2 years, 7 months ago

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– Finn Hulse · 2 years, 7 months ago

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?Log in to reply

– Deepanshu Gupta · 2 years, 7 months ago

Thanks,@Finn But how can I expressed \( v=f(x)\) or \(v=f(t)\).?? which is essential for this question. ( that is my Problem)Log in to reply

– Finn Hulse · 2 years, 7 months ago

I'm not sure I understand what you mean.Log in to reply

– Deepanshu Gupta · 2 years, 7 months ago

Is it possible to express the velocity as an individual function ?? or we require Higher mathamatics??Log in to reply

– Finn Hulse · 2 years, 7 months ago

Are you asking if you can solve for \(v\)? Because if you are, I think it would be very tricky.Log in to reply

– Deepanshu Gupta · 2 years, 7 months ago

yes.. will you please give a try to it ? I make all possible attempt but not succesfull in it.Log in to reply

– Finn Hulse · 2 years, 7 months ago

Sure. Also, I've been to Jaipur! It's super awesome! :DLog in to reply

"\(padharo\) \(mhare\) \(desh\)"

Well for what purpose you have been come here... is it Vacation's celebration or something else ? – Deepanshu Gupta · 2 years, 7 months ago

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– Finn Hulse · 2 years, 7 months ago

I took a trip around Rajasthan and also to Agra (for obvious reasons). I visited Delhi, Jaipur, Udaipur, Bundi, Chittogarth, Ranthambhore, and some other places. :DLog in to reply