problem

tony_parsons

d^2V/dt^2 + dV/dt = dV/dx

As x--> infinity, V --> 0

Find a seperable solution.

Thanks.

Reply 1

AlphaNumeric

10

Let V(t) = T(t)X(x)

Then just wack it in the equation. It's a bog standard seperable solution method. Just copy what you've got in your notes but you'll have to solve different differential equations, namely

\ddot{T}+\dot{T} = \lambda T

and

X' = \lambda X

Reply 2

Dwight67

AlphaNumeric

Let V(t) = T(t)X(x)

Then just wack it in the equation. It's a bog standard seperable solution method. Just copy what you've got in your notes but you'll have to solve different differential equations, namely

\ddot{T}+\dot{T} = \lambda T

and

X' = \lambda X

completely wrong. This is a common misconception, and the method you suggested is far too remedial. I have pmed the answer with explanations to you tony; hope it helps.

Reply 3

AlphaNumeric

10

Dwight67

completely wrong. This is a common misconception, and the method you suggested is far too remedial. I have pmed the answer with explanations to you tony; hope it helps.

Mmmm, quite. Unfortunately your particularly stellar brand of condescending humour is slightly lacking, given that that method is not 'remedial' unless you count the standard method of computing answers to seperable PDEs 'remedial' and does infact yeild an answer in about 4 lines of working.

But given it's clear from a search of your posts it's 'your thing' to post short, insulting and ultimately pointless points to get a raise out of people, I'm not bothered. Your post alone makes you look a prat without much effort from myself :smile:

Reply 4

robotix

prove by mathcal induction that d(x^n)/dx = nx^(n-1)

can any1 do this 4 me plzzz
thx very much

Reply 5

Speleo

7

prove by mathcal induction that d(x^n)/dx = nx^(n-1)

can any1 do this 4 me plzzz
thx very much

Assume (d/dx)(x^n)=nx^(n-1)
(d/dx)(x^n+1)=(d/dx)(x*x^n)
=x(dx^n/dx)+x^n(dx/dx) (product rule)
=nx^n + x^n
=(n+1)x^n

Then verify that it works for x= 1, which it does.