Analytical solution Definition and 61 Threads

Can anyone help me about analytical solution of this Integral? the integral is written in the word file attached here. Many Thanks in advance, Ashkan

I am trying to derive an equation of motion for a simple electrostatic potential well. Imagine a scenario where an electron (or other charged particle) is released from an arbitrary distance from a fixed (unperturbable) attractive charge (say a proton fixed in space). In 1 dimension, the...

LaTex Code: \frac{\partial U}{\partial t} + ax\frac{\partial U}{\partial x} + b\frac{\partial^2 U}{\partial x^2} = 0 Can someone please tell me how to solve this PDE? Thanks, Geoff

Hello everybody, I am a newbie in using Matlab and i have faced a problem i haven't been able to overcome so far,so i decided to share it with you. I would like to solve the following equation in Matlab: (-2*t...

I have the equation del^2 phi =1 for 2-d (x and y) with the boundary condition being 0 along all 4 edges. I've looked in all my math books and can't find how to solve this. If anyone could get me started I would appreciate it.

Analytical Solution to this? -- linear system of ODES Hi All, It's been awhile since I've even attempted to solve something analytically, so before jumping back into the text. Does the following already have a common solution that I can find somewhere? Thanks, dx1/dt = A1 + B1x1...

Hi, I'm trying to find an analytical solution of Laplace's equation: \phi_{xx} + \phi_{tt} = 0 with the tricky boundary conditions: 1. \phi(x=0,|t|>\tau)= 0 2. \phi(x\neq0, |t|>>\tau)=0 3. \phi_{x}(x=0, |t|<\tau)=-1 4. \phi_{t}(x, |t|>>\tau)=0 I have the following ansatz(I...

I have a couple ODEs that I need to solve. I was probably just going to put them into mathematica, but I like finding the analytical way also. The first one is \frac{d}{dx}\left( \frac{(y + \lambda)y'}{\sqrt{1+y'^2}} \right) = \sqrt{1+y'^2} Lambda is a constant and y' is dy/dx. I...

Hi there, Before i state what my actual question is, let me give some background on some work i have done on this. I have been trying to solve the 0-D PRKE transient problem for a step and a ramp input numerically using couple of high precision methods. 1) Using MATLAB's inbuilt ode23s...

Hello all, I wanted to know if there are ways to find analytical solutions for a set of equations defined as follows: 1) x''(z) + B(y,z)*y'(z) + C(y,z) = 0 2) y''(z) + B(y,z)*x'(z) = 0 where ' represents derivative wrt z. and we need to determine y(z) and x(z). B(y,z) and C(y,z) are...

im looking for an exact analytical solution for the following (1/alpha) * dT/dt = d2T/dr2 + (1/r)*dT/dr where d is actually dou(partial diff.) subject to the boundary conditions, a<=r<=infinity t>=0 T=Ts (constant) at t=0; -dT/dr + HT = H(Tf) at r=a; where H, Tf are...