I am currently trying to solve for the metric function for a black hole in adS space with quasi-topological gravity. The details aren't too important, but the point is that I have to solve for a cubic at one point, and choose the correct solution, which is the one that reduces to a linear...
I am trying to model the diffusion of fluorophores in a cell with a source in the middle by solving the appropriate differential equation. I can solve the PDE easily enough, however as I haven't done DE's in a while, I need a refresher on how to apply the appropriate boundary conditions for my...
I've tried your idea, and it looks like that's pretty much what I've been doing the whole time, so I can't see where I'm going wrong. Here's what I did:
Where am I going wrong? Thanks for the help!
I know how to do Frobenius on variable coefficient ODE's but only when the coefficients are powers of the independent variable. Can I do method of Frobenius on something like:
y'' + e-xy = 0 ?
What form would I assume a solution of? Just the regular y=sum(Akxk+r ?
Thanks for the help!
Homework Statement
Find the general solution to x'' + e^(-2t)x = 0, where '' = d2/dt2
Homework Equations
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The Attempt at a Solution
First I did a change of variables: Let u = e^(-t)
Then du/dt = -e^(-t)
dx/dt = dx/du*du/dt = -e^(-t)*dx/du
d2x/dt2 = d/du(dx/dt)du/dt =...
I am looking through my course notes for mathematical physics, in preparation for the exam, and I've run into a concept that I can't figure out. It comes up first when talking about the modified bessel's equation
(x^2)y''+(x)y'-(x^2+p^2)y=0
And supposedly this can be transformed into...
URGENT - Compton Scattering - Electron Momentum
Homework Statement
An x-ray photon of initial energy 1x10^5 eV traveling in the +x direction is incident on a free
electron at rest. The photon is scattered at right angles into the +y direction. Find the components of momentum of the...
Homework Statement
I am trying to plot the non tie-line paths for the solution to 3 component injection with constant K-values.
Homework Equations
The Attempt at a Solution
In order to construct the paths on a ternary diagram, I need to find C1 and C2. Then C3 = 1 - C1 - C2, so...
Bump!
I think I have the boundary conditions:
P(0,t) = some constant (non-zero, from Darcy's law)
P(L,t) = Po ??
P(x,0) = Pi or do I use dP/dx = 0 since the end is 'insulated'
Now I know how to solve pde's for both ends at 0 or both ends insulated, but not for one end at...
I'm trying to understand how to set up the problem of a 1D wire that is insulated at one end and has a heat source at the other. I know the heat law, from my textbook:
du/dt = B d2u/dx2 + q(x,t) 0 < x < L, t > 0
Where q(x,t) is the source of heat.
The problem is, I want the heat...
Homework Statement
I have been asked to model the flow of a slightly compressible liquid through a rigid, incompressible porous medium in 1D, assuming the flow obeys Darcy's law. I am given a rectangular prism of cross sectional area A with length L, a source of liquid (say water) on one...
Thanks so much for the help... this is really frustrating. Maybe I'm just making arithmetic errors, bu I just can't get the right answer. Using your method:
r=A cos^{1/2}(2\theta)
r'=A cos^{-1/2}(2\theta)sin(2\theta)
r'^{2}=A^{2}cos^{-1}(2\theta)sin^{2}(2\theta) =...
Thanks for the reply! But I am not sure what youre getting at.
When you say derive the second equation, I assume you mean differentiate it?
In that case, is this correct?
\dot{\theta} = L / mr\stackrel{2}{}
\ddot{\theta} = -2L\dot{r} / mr\stackrel{3}{}
Im a little unsure as to how...
Homework Statement
Homework Equations
on image
The Attempt at a Solution
The first thing I did was use the second equation to get
Theta dot = L/mr2
Which I then subbed into the first equation to eliminate Theta dot.
Now I need everything in terms of r, and this is...