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.

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

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?

Log in to reply

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 \(v = \frac {dx}{dt}\).

Log in to reply

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

Log in to reply

@Ronak Agarwal @jatin yadav will you help ??

Log in to reply

@Pranav Arora @Finn Hulse any Help??

Log in to reply

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

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

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

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

Log in to reply

Log in to reply

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

Log in to reply

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

Log in to reply

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

Log in to reply

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

Log in to reply

@satvik pandey Done..!!

Log in to reply