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

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

$UPDATE$ :

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

$v=f(t)$

$v=f(x)$ .

$Given$ .

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.

#Calculus #Physics #ElectricityAndMagnetism #Mechanics #HelpMe!

Easy Math Editor

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Comments

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?

Arif Ahmed - 6 years, 8 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 $v = \frac {dx}{dt}$ .