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Dec
4
reviewed Leave Open What is the degree of following differential equations
Nov
28
awarded  Custodian
Nov
28
reviewed Reviewed Iterative update of pseudo inverse solution
Nov
28
awarded  Custodian
Nov
28
reviewed Leave Open Assumed True until proven False. The Curious Case of the Vacuous Truth
Nov
25
revised Separating Partial Differential Eq
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Nov
25
comment Separating Partial Differential Eq
let us continue this discussion in chat
Nov
25
revised Separating Partial Differential Eq
texified it
Nov
25
comment Separating Partial Differential Eq
The separation I've shown you is correct. What is $a$ and $b$? As I told you, the relationship between $C$ and the separation constant comes from the boundary conditions. Why don't you edit your question and show us how did you derived the relation $a^2 + b^2 = C^2$? Here is a quick guide on how to typeset equations.
Nov
25
awarded  Informed
Nov
25
comment Separating Partial Differential Eq
Well, if by a relationship you mean $C = C(\lambda)$, then no. The solution of the system is \begin{align}\Theta(\theta) &= A e^{\sqrt{\lambda} x} + B e^{-\sqrt{\lambda} x} \\ R(r) &= C J_\sqrt{\lambda}(C x) + D Y_\sqrt{\lambda}(C x)\end{align} where $J_\sqrt{\lambda}$ and $Y_\sqrt{\lambda}$ are Bessel and Neumann functions of the first kind, of order $\sqrt{\lambda}$. If no boundary conditions are given, then you have an infinite collection of solutions spanned by both parameters.
Nov
25
comment Separating Partial Differential Eq
I'm guessing you're getting Helmoltz equation from separating time and space from a cylindrical wave equation. If you need to quantize $\lambda$ and $C$, then boundary conditions are needed.
Nov
25
answered Separating Partial Differential Eq
Nov
15
awarded  Yearling
Sep
10
comment Solution of a differentiation in integral form
@ComplexGuy Indeed.
Sep
10
comment Solution of a differentiation in integral form
@ComplexGuy It gets absorbed in the definition of $\hat{c}_1(k)$. I abused the notation, sorry!
Sep
10
comment Solution of a differentiation in integral form
@ComplexGuy When $t=0$, $\sin(\omega t) = 0$, and the equality follows.
Sep
10
revised Comparison between Bessel's coefficients
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Sep
10
answered Comparison between Bessel's coefficients
Jul
22
comment Perturbation Theory on Finite Domains
You should read about the WKB approximation. A great treatise on the asymptotics of $y'' + p(x) y = 0$ can be found in chapter 6 of Olver's Asymptotics and Special Functions.