Differential Equation: dv/dx Solution

[nishant]

please try to solve: dv/dx={kx/v}[e^{-x/vRC}]

 

[dextercioby]

It doesn't look good.I'll let you know why

-\frac {1}{2xk}v^2 e^{\frac {x}{vRC}}-\frac {1}{2RCk}v e^{\frac {x}{vRC}}-\allowbreak \frac {1}{2}\frac {x}{R^2C^2k}\mbox{Ei}\left( 1,-\frac{x}{vRC}\right) +v=C

Daniel.

 

[nishant]

sorry but what is Ei?

 

[dextercioby]

Exponential integral,http://mathworld.wolfram.com/ExponentialIntegral.html,what else.

Daniel.

 

[saltydog]

Nishant, would you kindly supply some reasonable values for k, R, C, and a reasonable initial condition so I could plot it to see what it looks like.

Thanks,
Salty

Edit: I mean numerically (via Runge-Kutta). I dont' think I could plot it using the implicit solution.

 

[nishant]

K,R,C are constants

 

[dextercioby]

He knew that,he was asking for numbers.

Daniel.

 

[saltydog]

You know Nishant, I shouldn't give you the impression that I "need" reasonable values to plot it. Really, I can just pull them right out of thin air to get a plot: Wait . . . .1,1,1, and another one. See, got a plot. Really though, might be interesting to study how the solution varies as the constants change unless you have a particular set up in mind.

Edit: Here it is, see, 1, 1, 1 and . . . well, you know.

 

[nishant]

I am not able to understand Ei,how do u write it in mathematical form?

 

[dextercioby]

Well,how did u run into that equation in the first place...?

Daniel.