Separation Definition and 448 Threads

To solve a separable ODE like this I would simply multiply each side by dx and then integrate both sides. However, I know that it is only notational convenience that allows me to do this, and what's really going on is slightly more complicated. Take this DE for example...

Homework Statement Knowing that the wave function of the hydrogen atom is proportional to e-r/a0, estimate how t depends on the proton proton separation d. I need just to make a drawing of the integrand and make a reasonal approximation using my intuition (no numerical methods allowed to...

Homework Statement fringes are observed when a parrallel beam of light of wavelength 500nm is incident perpendiculary onto a wedge-shaped film with an index of refraction of 1.5. What is the angle of the wedge if the fringe separation is 1/3cm? Homework Equations t(x)=xtan(theta)...

Good day, I have to separate the variables of the formula (dy/dx) + 1 = - (y/x) so I can determine the solution of the differential equation. I get: (dy/dx) + 1 = - (y/x) (dy/dx) = - (y/x) - 1 (dy) = (- (y/x) - 1)dx Though I cannot get rid of the y at the side of dx...

For those who have the book, in corollary 19.6 page 234 of Bredon, the Jordan-Brouwer separation theorem has just been proven and so we know that if S is homeomorphic to S^(n-1), then S^n\S has two connected components, which are open in S^n and their boundary is S. So we let V be one of the...

Homework Statement the question is:calculate angular separation between 1st order red and 1st order violet.data given:theta=22,d=1.20x10^-6 Homework Equations theta=a/D ( is that the 1?) and if it is dn what would the function be hmm tan? (isnt it related to stellar distances) The...

Homework Statement Two protons that are very far apart are hurled straight at each other, each with an initial kinetic energy of 0.19 MeV, where 1 mega electron volt is equal to 1106 (1.610-19) joules. What is the separation of the protons from each other when they momentarily come to a...

Suppose that a binary-star system consists of two stars of equal mass. They are observed to be separated by 350 million {\rm km} and take 5.4 Earth years to orbit about a point midway between them. I got 1.1x10^29 as my answer, but it is incorrect. Can anyone help me out?

Electromagnetism just got weird. REALLY weird. Everything was going great until we hit this new chapter on separation of variables. I don't remember doing this kind of stuff in my DiffEqs class. Frankly, I'm feeling overwhelmed. I have a midterm at the end of this week, and I feel as though...

Hello, I have the following problem with respect to fluid mechanics: A source of strength Q is in a 3D space and subjected to a parallel flow U along the x-axis. The position of the source is at (xq,yq,zq). This will lead to the following velocity potential in cartesian and cylindrical...

Hello If you had an aqueous solution of phosphates, nitrates and nitrites, how could you separate them? Also, if not answered above, how could you separate a solution of just nitrates and nitrites? thank-you for you're time

Homework Statement There are six object. First five are the same and carrying charge Q, the last one is uncharged. Let the first object touch with the second one, the uncharged one obtain x unit of charge. What 's the total charge will the last object get if we let the rest four objects...

"A sphere of homogeneous linear dielectric material is palcced in an otherwise uniform electric field E. Find the electric field inside the sphere." Griffiths uses separation of variables to solve laplace's equation in the interior of the sphere. I have two questions. (1) How can you try...

Ideally, should we only allow athiest to hold public office? This way assuring the separation of church and state? (I was going to use the poll option but it doesn't seem to be working).

I was watching Law & Order and I realized a blatant violation of the separation of church and state. (1) When you swear to tell the truth, you put your hand on a bible. (2) When you talk to a preist, they are legally allowed to not repeat what you told them in confession, even if you...

Homework Statement Solve the 2-D time-independent Schrödinger equation with V (x,y) = 0: Homework Equations -ћ2/2m ( ∂2Ψ(x,y)/∂x2 + ∂2Ψ(x,y)/∂y2 ) = EΨ(x,y) The Attempt at a Solution I started by getting -ћ2/2m to one side: ( ∂2Ψ(x,y)/∂x2 + ∂2Ψ(x,y)/∂y2...

Hi, I have a question about separation of solid mixture by extraction. so how can you tell what reacts with what and which layer contains what? k for example, if you have a mixture of phenol and salicylic acid, first the mixture is dissolved in diethyl ether... then the solution is mixed with...

There is a spaceship in low-earth orbit, at 2000km above the surface of the earth. There are two balls in the spaceship that are dropped. The balls are 1m apart. How long will it take for their separation to increase to 1.01m? Assume that one ball is at 2000km, and the other is at 2000km+1m...

when separating mixtures using only physical methods, does the order in which you separate them mater? for example, if i had had urea and napthalene in the mixture...both are water soluble...so to take the urea out i first take out the napthalene through sublimitation and then the urea...

Homework Statement so here's my equation: dy/dx=(xy+3x-y-3)/(xy-2x+4y-8) so what i did first was factor out the right side =(x+1)(y-3)/(x+4)(y-2) then i did a bunch of manipulation to get the ys on one side and the xs on another (i won't write this out right now but if anyone...

One particle has a mass of 3.00 10-3 kg and a charge of +7.80 µC. A second particle has a mass of 6.00 10-3 kg and the same charge. The two particles are initially held in place and then released. The particles fly apart, and when the separation between them is 0.100 m, the speed of the 3.00...

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Homework Statement Two positive point charges are held in place, 0.86 m apart. They are then moved so that their electric potential energy doubles. What is the new separation between the charges? Homework Equations kq/r The Attempt at a Solution had PEb=KQaQb/d=2EPEa, then did...

Homework Statement Not sure if you guys can get this link http://www.maths.uwa.edu.au/devsite/Units/math3341-s1-2008-crawley/assignments-solutions/Sheet%204 should be able to. Question is question two.Homework Equations Not many besides the general separation of solutions sort of thing but I...

Homework Statement y'=xsec^2(x^2) 2. The attempt at a solution dy/dx=xsec^2(x^2) dy=xsec^2(x^2)dx \intdy=\intxsec^2(x^2)dx lny= (here i'll do a u substitution) ---- u=x^2 du=1/3x^3dx ... and here's my problem. It seems like that creates a very difficult u-sub to try and manage...

\left[\begin{array}{c} y'_1(x) \\ \vdots \\ y'_n(x) \\ \end{array}\right] = \left[\begin{array}{ccc} f_{11}(y) & \cdots & f_{1n}(y) \\ \vdots & & \vdots \\ f_{n1}(y) & \cdots & f_{nn}(y) \\ \end{array}\right] \left[\begin{array}{c} g_1(x) \\ \vdots \\ g_n(x) \\ \end{array}\right] If n=1, then...

Homework Statement Two bodies move in a straight line towards each other at initial velocities v1 and v2 and with constant retardation a1 and a2 respectively at the initial instant. What is the max initial separation between the bodies for which they will meet during the motion? (sqr ->...

I would use the entire template except this question is very simple and does not require all of it. Homework Statement How do I separate \frac{X''(x)}{X(x)}+\frac{Y''(y)}{Y(y)}=\sigma into ordinary differential equations when \sigma is a constant. Thanks for your help!

Hello ! I'm having a hard time finding the exact hypotheses which would allow me to use the separation of variables method for partial differential equations. I want a clear statement telling me 'when you have that very kind of partial differential equation (with precise boundary and...

Homework Statement Sorry for the mis-spelled title - it's "series". Please take a look at http://www-solar.mcs.st-and.ac.uk/~alan/MT2003/PDE/node21.html In step 2.60, when he wants to find the coefficient B_n, the argument in the sine-function does not contain a "2". In my book, the...

Homework Statement Please take a look at: http://www-solar.mcs.st-and.ac.uk/~alan/MT2003/PDE/node21.html Look at step 2.53. Can you explain to me how c^2*T'/T = k becomes T' = k*T*c^2? The Attempt at a Solution I don't get it. What am I missing here?

Homework Statement Using separation of variables determine if the solution escapes to infinity in finite time or infinite time? y'(t)=1+\frac{y(t)}{2} y(0)=.5 Homework Equations Knowing how to do separation of variables.The Attempt at a Solution Here is my attempt, but I get stuck...

Hi guys, just wondering whether you could help. I've got a complex number in terms of a lot of variables, and need to separate it into its real and imaginary parts. How do I do that? I spent past hour trying to look for tutorials, unfortunately none tells you how to do it...

When a space shuttle launches, how is simultaneous SRB cutoff assured so as not to create an asymmetrical thrust situation? (assuming that SRB cutoff occurs prior to separation). Thanks, FRQ

Not sure if I'm in the right forum, but does anyone know anything about the mechanism behind using radio waves to disassociate hydrogen and oxygen atoms from salt water?

[SOLVED] Capacitance vs. Distance of separation Homework Statement Hi, I am suppose to make a capacitance vs (1/d) graph. I understand that the relationship between the capacitance and distance between the plates is inversely proportional and that it does not produce a straight line. My...

Homework Statement Find an implicit and explicit solution for the given initial-value problem \frac{dx}{dt}=4(x^2+1) for x(\frac{\pi}{4})=1 \frac{dx}{dt}=4(x^2+1) \Rightarrow \frac{dx}{x^2+1}=4dt \Rightarrow \tan^{-1}x+C=4t Now I am a little stuck. Usually I just plug in my...

My book has a problem that requires you to separate variables (one side has all the y terms and one side has all of the x terms): \sin{xy'}=\cosx Equation after separation of variables: dy=\cot{x}dx My question is, how do you know that the y' is contained within the sine function or...

I do not understand the process of separating variables such as in derivatives. I thought that dy/dx is just the rate of change of y with respect to the independent variable x. Why can you physically move dx (like multiply it on both sides)?? What would "dy" be reffered to as then? Simply the...

In pde, it seems to me all kinds of equations about nature phenomena have the property that time and space derivatives are separate. For example, u_t = u_xx, heat equation. So I wonder, is that always the case in nature? I mean, do you guys ever see equation describing real nature mechanism...

entropy increases? entropy decreases ? no change in entropy? diffusion, evaporating, mixing, melting, separation i think diffusion - increase evaporation - increase mixing - increase melting - increase but what about separation :S? and if anyone thinks any others are...

u(r, θ) satisfies Laplace's equation inside a 90º sector of a circular annulus with a < r < b ; 0 < θ < π/2 . Use separation of variables to find the solution that satisfies the boundary conditions u(r, 0) = 0 u(r, π/2) = f(r) ; a < r < b u(a, θ) = 0 u(b, θ) = 0 ; 0 < θ < π/2 Consider all...

1) Hydrogen’s electron and proton are separated by 5.3x10-13 meters. What is the electrical force between them? 2) A charge moved .02 meters in an electric field of force 215 N/C. If the electric potential decreased by 6.9x10-19, what is the charge of the particle? 3) If a capacitor...

So it was basic to figure out the masses and such, but I'm not exactly sure what the "orbital separation" really is? Can someone enlighten me? Here is the question for reference: A moon with a mass one quarter that of its parent planet orbits that planet with a period of 12 days. The mass of...

No idea where to start with this one, any help is much appreciated... "A metal plate needs to be reduced to a thickness of 4 cm by involving a rolling mill. After rolling, the elastic properties of the material cause the plate to regain some thickness. Calculate the needed separation between...

Homework Statement Two particles A and B are projected from the same point O with angle speed 30degree from the horizontal. If A has the speed of projection equal to (7)^0.5m/s and B has twice the projection speed,find the separation between them,when their velocities are mutually perpendicular...

Hello, I want, for obscur reasons which would lead us too far to explain, to split my flow into two component, one steady and another one non-steadyv = v_0 + v' I'm looking for a simple equation governing the evolution of this non steady components. The complete momentum equation gives...

Homework Statement The temp. as a function of time of a metal rod obeys the following diff. eq. \alpha^2 \frac{\partial^2u(x,t)}{\partial x^2} = \frac{\partial u(x,t)}{\partial t} Use separation of variables to find u(x,t) in a rod of length 1 subject to the conditions u(0,t) = 0 ...

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Homework Statement The edges of a square sheet of thermally conducting material are at x=0, x=L, y= -L/2 and y=L/2 The temperature of these edges are controlled to be: T = T0 at x = 0 and x = L T = T0 + T1sin(pi*x/L) at y = -L/2 and y = L/2 where T0 and T1 are constants...