# Help in Solving Physics Differential equation.

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.

UPDATE

Note by Deepanshu Gupta
3 years, 9 months ago

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In 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?

- 3 years, 9 months ago

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 $$v = \frac {dx}{dt}$$.

- 3 years, 9 months ago

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

- 3 years, 9 months ago

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

- 3 years, 9 months ago

@satvik pandey Done..!!

- 3 years, 9 months ago

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

- 3 years, 9 months ago

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

- 3 years, 9 months ago

@Ronak Agarwal @jatin yadav will you help ??

- 3 years, 9 months ago

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

- 3 years, 9 months ago

@Pranav Arora @Finn Hulse any Help??

- 3 years, 9 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?

- 3 years, 9 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)

- 3 years, 9 months ago

I'm not sure I understand what you mean.

- 3 years, 9 months ago

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

- 3 years, 9 months ago

Are you asking if you can solve for $$v$$? Because if you are, I think it would be very tricky.

- 3 years, 9 months ago

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

- 3 years, 9 months ago

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

- 3 years, 9 months ago

wow.. !! A very warm welcome to you for coming in Jaipur..... In our Language we says:

"$$padharo$$ $$mhare$$ $$desh$$"

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

- 3 years, 9 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. :D

- 3 years, 9 months ago