# separation

1. ### Clever version of separation of variables

I came across a very interesting method to "separate" variables in an eigenvalue equation. But I'm not quite sure it works as advertised. Here's the sitch. We have, as usual: H \Psi = E \Psi, where H is dependent on both radial and angular variables, so we expect \Psi to contain both radial...
2. ### Plane Separation Postulate Help

We learned about half plane geometry today and I am having a hard time with this proof. Any help is appreciated.
3. ### Doubt on the Axioma of Separation (Russel's Paradox)

How can this evade Russel's Paradox? If p is a property, for any X, there exists a set Y = {x E X;P(x)} If P(x) = x ~E x (a set x cannot contain itself) ^ Y = x Then Y E X ^ Y ~E Y A paradox: Y E X and Y ~E Y cannot coexist

5. ### Separation of Variables

Im having trouble separating functions into the form q(y)dy=p(x)dx. It seems like they should be simple but im stuck on these. Any help would be appreciated. Thanks. Here are two examples \frac{dy}{dx}=\frac{y^2+1}{xy+y} I can only get this far.. ydy=\frac{y^2+1}{(x+1)}dx and im also having...
6. ### Separation of variables

Hi, I have this problem, but I am stuck in one thing. Assuming that solutions to y_{tt}=g(zy_z)_z are of the form y(z,t)=Z(z)T(t), and that the separation constant is negative, written as -v^2 with v>0, I need to show that Z(z) and T(t) must satisfy the differential equations T''+v^2gT=0, and...
7. ### Applying the method of separation of variables.

The Equation :- iR + L \frac{di}{dt} = E whereR,L and E are constants arises in electrical circuit theory.This equation can be solved by separation of variables. Find the solution which satisfies the condition i(0) = 0
8. ### Integration using separation of variables

Integrate the following integral using separation of variables : vx = (1/3)v -(8/9) (vx is the partial derivative of v w.r.t x) and v is a function of two variables. Can someone please show me the steps involved for separating the variables for this question ? Please Help.
9. ### PDE problem - Separation of variables - Dirichlet condition

[Solved] PDE problem - Separation of variables - Dirichlet condition Hi all I'm in quite some trouble with this PDE problem, that is part of my assignment for wednesday. First of all I got the PDE problem: PDE: u_t - 2*u_xx = 0 , 0<x<1, t>0 BC: u(0,t) = t, u(1,t)=0 IC...
10. ### Separation of variable/partial fractions

So I was presented a problem with 3 components; the first 2 I believe I've done right; but I need a bit of push for the 3rd component: dP/dt = (r/K)(P PU )(PS P) where P(t) is the population size, r is the intrinsic reproduction rate, K is the carrying capacity, PU is the unstable equilibrium...
11. ### Separation of Variables

Hello, I'm a little stuck on this problem: Find a solution to the differential equation subject to the initial conditions. dz dt = tez , through the origin. Here is how I tried to solve the problem: dz dt = tez multiply both sides by dt, and then divide both sides by ez...
12. ### Solving Poissons equation with a delta function in RHS using separation of variables.

Hi Everyone, I am trying to solve the partial differential equation given below: \Delta^2\phi(x,y,z)=\frac{qf(x,y,z)}{\epsilon} where f(x,y,z)=1 at one point and zero elsewhere. This is the poisons equation for a point charge inside a conducting box. Can this be solved using the variable...
13. ### Demonstration for separation of variables

Hi there. I have to demonstrate that if an ordinary differential equation is susceptible to separation of variables, then its an exact differential equation. This is what I did: If it is separable then: g(y)dy=f(x)dx \rightarrow g(y)dy-f(x)dx=0 If and only if: \frac{\partial g}{\partial...
14. ### Applied Math: Beam Deflection using Separation of Variables

Beam's dynamic deflection is governed by the following PDE EI(∂^4w/∂x^4)+(rho)*A* (∂^2w/∂t^2)=f(x,t) where E = the modulus of elasticity, I = the moment of inertia, p = mass density, A = cross-section area, w(x,t) = deflection, 0 ≤ x ≤ L = axial coordinate, L = length, t = time. The load is...
15. ### Separation in differential equation

How can I get a separate y, y' and y'' in equation (y')^2 + y*y''+y'*y = 0 Best regards (Shake)
16. ### simple integral separation problem

If I know that: \frac{dk}{dl}=\frac{w}{v} Then does it follow that: dk=\frac{w}{v}dl \int 1 dk=\frac{w}{v}\int1dl \frac{k}{l}=\frac{w}{v} ? Thanks
17. ### Separation of variables problem then satisfying initial condition

If y(t) is such that dy/dt = 13(t^3)(y^2), y(0) = -4, then compute y(1). i know your suppose to switch it up such that dy/(y^2) = (t^3)dt ... and then you take the integral of both side and get (-)1/y = 1/4(t^4) + c.... and then its this part where i screw up on the correct algebra per say...
18. ### Having problem with this separation

I'm pretty sure I'm doing something wrong. the question is: Formulate the general solution to the differential equation. (express in y^2 in terms of x) dy/dx = e^x/y + 2y This is what I did doing so far. dy/dx = e^x/y + 2y dy/dx - 2y = e^x/y dy/ydx = e^x +2 dy = y(e^x...
19. ### Simple Separation of Variable Problem

I'm just starting a course in DiffEQ and we have a simple separation of variables problems. The problem is to change the dy/dt equation into a simple y(t) equation (example dy/dt=ty becomes y=k*e^(t^2)) where k is any real number). The problem I am stuck on is dy/dt=t/(y+y*t^2). Here is my...
20. ### Separation of two places

I need to find the angular separation between two points on the earth's surface. The points are as follows: 40.99N, 44.19E and 22.33N, 114.18E. I have done the maths and got 60.8 degrees. It can't be the case since 114.18-44.19 is already 69.99 degrees. Here's what I did pls tell me what's...