Modified Bessel Equation
Hey all, I wanted to know if anyone knew somewhere I could find the asymptotic behavior for small x (i.e x approaching 0) limit of the modified Bessel equations with complex order. The wikipedia page...
View ArticleDifferential Equations For Solving A Recursive equation
Hi, i have a question about a proof of some recursive equation, the function is $$c_{n}(a)=\int_{0}^{\pi } \frac{cos(nx)-cos(na)}{cos(x)-cos(a)}$$ whit ##n\in \mathbb{N}## and ##a\in \mathbb{R}## ....
View ArticleS9.3.a de with u subst
Solve the de $$\dfrac{dy}{dx}=\dfrac{1}{7}\sqrt{y}\cos^2{\sqrt{y}}$$ sepate variables $$\displaystyle \dfrac{dy}{\sqrt{y}\, \cos^2{\sqrt{y}} }=\dfrac{1}{7}\, dx \implies...
View ArticleMatrix Methods for Difference Problems
I'm looking at ways of solving 2nd order difference equations with non-constant coefficients. I am working on a method to use transformations (ie rewriting the equation in new variables) to change the...
View ArticleMatrix Methods for Difference Problems II
This is related to a recent (mainly unserious) post I recently made. I did some more work on a similar problem and I'd like to bounce off an idea why this doesn't work. I really am not sure if I'm...
View ArticleHow to make the deflection equation at any point along a snow ski profile?
I am trying to figure out how to do a deflection profile for a snow ski profile at 50 mm increaments along the ski. Since the ski has different widths and heights at each crossection, the EI changes at...
View ArticleFEM Method in 2D with Triangular Elements
I have worked through the basics of the FEM method in 2D with rectangular elements and now am trying to learn triangular elements but need a simple enough numerical example. It seems triangular...
View ArticleRecurrence relations for series solution of differential equation
I am currently looking at section IIA of the following paper: https://arxiv.org/pdf/gr-qc/0511111.pdf. Eq. (2.5) proposes an ansatz to solve the spheroidal wave equation (2.1). This equation is $$...
View ArticleBessel Functions Cheat Sheet
This is a helpful document I got from one of my DE's teachers in graduate school, and I've toted it around with me. I will type it up here, as well as attach a pdf you can download. Bessel Functions...
View ArticleSturm-Liouville Problem Cheat Sheet
This is a helpful document I got from one of my DE's teachers in graduate school, and I've toted it around with me. I will type it up here, as well as attach a pdf you can download. THEOREM: Consider...
View ArticleInexact Differential Equation with 4 Degree
hello ... I wanted to demonstrate the solution of a differential equation, and as I do not yet know the latex language, then I take pictures of the leaves with my solutions ... the user who wants to...
View ArticleInterpreting a proposition
Could someone help me interpret the following proposition? I've been struggling to comprehend it. Thanks in advance. Proposition: If $J \subset \mathbb{R}$ is an open interval containing the origin and...
View ArticleDrawing Direction Fields for Higher Order ODEs
Hello : Trying to find references on drawing direction fields of higher order differential equation by hand as 1st step then by computer , do you know any reference I can read ( PDF , books ,...) , and...
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Quick Change of Variables Question
Hey all, I am currently struggling with a change of variables step in my calculations. Suppose the solutions ##f_{1}(x)## and ##f_{2}(x)## of the following system of differential equations is known:...
View ArticleReal ODE yields real solution through complex numbers
Hello, I'm posting here since what follows is not about homework, but constitutes a personal research which underlies some more general questions. As with the infamous "casus irreducibilis" (i.e....
View ArticleGeneral solution of 1D vs 3D wave equations
For the 1 dimensional wave equation, $$\frac{\partial^2 u}{\partial x ^2} - \frac{1}{c^2}\frac{\partial ^2 u }{\partial t^2} = 0$$ ##u## is of the form ##u(x \pm ct)## For the 3 dimensional wave...
View ArticleWhen should you use more mesh elements in the finite element method?
the simple rectangular isoparametric element (curved edges element) can be used to generate many complex shapes like.. square to circle square to triangle two square elements to annular. and the...
View ArticleHypergeometric Limits: Analyzing p(x)
I have been working with some Hypergeometric functions whose behavior I am not quite familiar with. Suppose the equation I wish to analyze is ##p(x) = (e^{x}-1)^{2i}\left({}_{2}F_{1}(a,b;c;e^{x}) +...
View ArticleBessel functions of imaginary order
In Wikipedia article on Bessel functions there is an integral definition of “non-integer order” a (“alpha”). For imaginary order ia I get that Jia* = J-ia, where * is complex conjugate and ia and -ia...
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Solve the homogenous Neumann problem
I am going through this notes and i would like some clarity on the highlighted part...the earlier steps are pretty easy to follow... Is there a mistake here...did the author mean taking partial...
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