This is my working: download.jpg

(Note that in my working: Fo = Fourier's Number = 1/CC and Bi = Biot's Number = h.(del r) / k).

Equation 4 is for the nodes along the central axis and I am not sure why it has been expressed as a summation of 10 nodes, when there appears to be only five conduction faces for the central element, as shown in Figure 1?

Anyone able to help with the steps I am missing would be much appreciated!

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I was reading in a physics book where we want to solve this differential equation:

I guess it is difficult to solve directly so they examined asymptotic behavior:

The thing what I did not get is equation (4.60). It will be nice if some one helped me to understand how they did this step.

Thanks.

So I'm fairly new to differential equations and this is my first time dealing with one of second order. Therefore if the problem seems easy that's why.

I am supposed to rewrite or reduce the following equation to a system of 1. order differential equations

y''-0.1*y+2=0

and then find a numerical solution where the following is true

y(0)=10 and y'(0)=-1

I'm not necessarily looking for a solution, but rather if someone could forward me to some kind guide or lesson about this. ]]>

I have a problem with solving the following equation. I need to log-linearize it around the steady state so I can use it in DSGE model as a linear equation. However, every time I try to solve it, exponentials

Thank you!

equation_13.PNG

* B_0, B_1, xi and phi are parameters

*

I've spent all day trying to find it, please help me. ]]>

I am trying to learn how to solve three dimensional Schrödinger Equation in Spherical Coordinates. I was reading a text book and I found that there is a missed step in the solution. Please see the attached picture. It says that the solution of equation (4.25) is not simple. It gave it directly as equation (4.26). Can you help me to learn how to solve such differential equations or at least guide me to some sort of text book or lecture notes that might help.

Thank you.

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I was reading the solution of Schrödinger equation for one dimensional harmonic oscillator. Please see the picture below. Every thing was going fine till equation (0.24) I could not understand how equation (0.23) can be written as equation (0.24). please help

Thanks

recursion formula.jpg

. . . . .[tex]\left|\dfrac{d}{dx}\right|\, \bigg(\left(3y\, =\, \sqrt{\strut -(u\, -\, 1)^3\,}\, -\, \sqrt{\strut (u\, +\, 1)^3\,}\right)\bigg)\, u\, =\, 2x[/tex]

Find the extremal of the functional:

If Euler's theorem is to be followed, I computed the condition:

to be:

However, I am not able to solve the DE any further. Please guide me. ]]>